Both the Danube and the Rivers marked the northern frontiers of the Roman Empire the fifth century, while the former continued, at least intermittently, to be the European border of the "Byzantine" Empire.
After the fall of the Western Empire, both banks of the Rhine became the domain of speakers of Germanic languages and dialects. In the early modern era, the increasingly centralized French Kingdom attempted to expand towards the Rhine, especially under Louis XIV, in order to break the Hapsburg encirclement and give a larger buffer to Paris. During the French Revolution, the concept of the "natural borders of France" (those being the Rhine, the Alps and the Pyrenees) was formally developed and achieved until Napoleon's defeat (he even had been offered to keep everything west of the Rhine before the defeat that preceded his first abdication).
Notwithstanding French ambitions, some brought opposite arguments:
From The Nation (New York), an argument in 1870 that rivers can never form "natural" boundaries between nations:
NATURAL BOUNDARIES
By Michael Heilprin
(September 1, 1870)
When the power of Napoleon I was rapidly crumbling away after the crushing defeat at Leipzig, the allies, halting at Frankfort before entering upon the last campaign, offered him, for peace, the undisturbed possession of France, with her limits extended east to the banks of the Rhine. The France thus offered him would have been almost coextensive with ancient Gaul, which was bounded by the Rhine, the Alps, and the Pyrenees, and would have embraced, besides the French Empire as it now is, the whole of Belgium, portions of the Netherlands, Luxemburg, and Rhenish Prussia, Hesse, and Bavaria. Napoleon, in his unreasonable pride, spurned these terms of peace, and when, a few months later, he presented them as his own to the Peace Conference at Chatillon, they were rejected by the allies. Napoleon fell, and the kingdom of the Bourbons was ultimately reconstructed as it had been before the wars of the Revolution. But since that time France has not ceased dreaming and talking of her natural boundaries — the Pyrenees, the Alps, and the Rhine. And this has not been the idle dream and idle talk of popular vanity and demagogism merely; statesmen, historians, publicists, and poets have vied with each other in making France believe that she had a natural right to all the lands west of the Rhine, and the dire consequence of that fondly cherished delusion is the present war.
We call it a delusion, for the Rhine is not a natural boundary of France in a rational sense of the word. Nor are rivers, in general, the natural boundaries of countries. Rivers, it is true, form excellent geographical lines of demarcation between provinces or other divisions of one and the same empire, kingdom, or confederation, such as are the lines of the Ohio and the Mississippi, which bound some of our non-original States. But they are no more real lines of separation than are the meridians of longitude or parallels of latitude which have been selected to bound other States of our Union. For rivers, especially navigable rivers, far from being separating barriers, are natural channels of intercourse and intermingling, of coalescence and union, the world over. Comparative geography, a science of rather recent development, has fully established this axiom. If used as real barriers, as the Rhine and Danube were by the Romans against the barbarians, and the Ticino and Po by the Austrians against Italy, they form unnatural barriers — that is to say, unnatural boundaries — kept up and guarded by the sword of the conqueror, occasionally long enough to become, or at least to appear, natural. Watersheds, not rivers, form natural boundaries. Mountain ranges separate nationalities. The same nationality almost everywhere flourishes on both banks of every navigable river. Every basin, or at least every section of a basin, has its character. The inhabitants of the slopes that hem it in will fuse with the dwellers in the bottom. People living on the opposite slopes of a mountain range will tend in opposite directions.
The whole of history and geography, studied together, proves it. The Nile has never nourished two different nationalities on its opposite banks; it has never been the boundary of an empire. Babylonia flourished on both sides of the Euphrates; Assyria on both sides of the Tigris. The Hebrews occupied both banks of the Jordan. Neither the Oxus nor the Jaxartes, neither the Indus nor the Ganges, neither the Yang-tse-kiang nor the Hoang-ho, has ever formed a boundary between different nationalities, or separated different civilizations. It was not the river Eurotas, the Alpheus, the Cephissus, or the Peneus, but mountain ranges like the Taygetus, the Pindus, and the Œta, that formed, by bounding, the wonderful system of Grecian autonomies. The various sections and branches of the Apennines mainly separated the ancient national divisions of Italy. Rome developed its power on both banks of the Tiber; the Po, in forming Cispadane and Transpadane Gaul, bounded provinces but separated no nationalities; the little rivulet Rubicon only marked the end of a frontier line formed by the Apennines, just as the little Tweed in the Middle Ages served to complete the natural boundary line of the Cheviot range between England and Scotland.
Mountain ranges, not rivers, formed, in the Middle Ages, the grand divisions of the Iberian Peninsula. The Ebro flows not on the confines but through the midlands of Aragon; the Guadalquivir does not bound but traverses Andalusia; Castilians live on both sides of the upper Douro and Tagus, Portuguese on both sides of the lower. The countries of Eastern and Central Europe show striking parallel examples. Russians inhabit both banks of the Volga and the Don, Poles both banks of the Vistula; Germans both banks of the Oder, the Elbe, the Weser, and the Rhine. The Danube flows through the very centres of Wurttemberg, Bavaria, Austria, and Hungary. The last-named polyglot country owes its national unity mainly to the encircling wall of the Carpathians; all its rivers flow towards or through its central bottom lands, and thus keep up a union even of the most heterogeneous elements. Bohemia is a mountain quadrilateral. . The mountain and river systems of the rest of Europe confirm the rule, with hardly a single exception. Neither do those of America invalidate it. That the Father of Rivers is a mighty bond of union instead of a barrier of separation, is acknowledged on all hands. The same is the case with the Missouri. A glance at the map will show that the St. Lawrence is only a figurative boundary line between the United States and the British Provinces, and that it flows through the latter. The Rio Grande is a frontier line dictated by recent conquest, and Indian tribes continue to roam on both its banks. Rivers selected as State lines are too feeble even as barriers between communities. The lower western bank of the Hudson is lined with suburbs of New York City. Camden is a suburb of Philadelphia; Covington, of Cincinnati. In South America, the Amazon and the Orinoco offer parallel instances to the Mississippi and the St. Lawrence. Some branches of the La Plata alone can be said to form exceptions, but recent events indicate that even these are not to last.
To return to the natural boundary between France and Germany. It is clear that the Rhine is far from forming it, either geographically or historically. The natural geographical boundary line, irrespective of the now existing nationalities, is the watershed between the Meuse and the Aisne and Marne, and its easterly continuation between the head-waters of the Saone and Doubs, on one side, and those of the Moselle and Ill, on the other. All of France that lies east and northeast of this watershed — the main parts of Lorraine and the whole of Alsace — belongs to the water-system of the Rhine, a river both banks of which, from its source to its mouth, are inhabited exclusively by Teutonic people — Swiss, Germans proper, and Dutch. Historically, the lands watered by those western affluents of the Rhine formed, after the downfall of the Roman rule in Gaul, parts of the Frankish realm of Clovis, and subsequently of its eastern and purely German division, Austrasia, while the valleys of the Seine and of its numerous affluents formed the much more Gallic western division, Neustria. The Carlovingian Empire embraced both divisions, but after its final disruption during the period of partitions inaugurated by the Treaty of Verdun, Austrasia was merged in Germany, while out of Neustria gradually grew up the modern Kingdom of France. And both Alsace and Lorraine — the latter in its main parts — continued to belong to Germany down to the time when French centralization, developed by Louis XI and perfected by Richelieu, proved itself decidedly superior to the more and more loosening machinery of the Empire — the final annexation of the two provinces to France taking place under Louis XIV and Louis XV respectively. The inner territories of Lorraine have since become almost entirely Gallicized; Alsace is French in sentiment, though not in language, and the section of the Rhine which bounds it on the east has assumed the semblance of a natural boundary, but the semblance only. The possession of the western bank of this river section has stimulated the desire of making the Rhine the eastern boundary of France. The constant threatening to achieve this conquest as an act based on a natural postulate has awakened, even in the more moderate portions of the German people, the thought of reestablishing, on an opportune occasion, the natural boundaries between Germany and France as they were before the Peace of Westphalia. It is beyond the sphere of this article to discuss the questions whether the present is the opportune moment to do it, and whether it would at any time be just or expedient to do it against the will of the populations concerned.
Heilprin's arguments sound quite convincing. Indeed most major rivers harbor the same cultural groups at their opposite banks. But let's take a closer look at the Danube. As Heilprin stated, this mighty river does indeed flow through the centers of Wurttemberg, Bavaria, Austria, and Hungary. He, however ignores the Lower Danube, which, by then, marked the border between Romania and Ottoman Bulgaria. Sure, Romania was still a Ottoman tributary, but it had different ethnic groups at its opposite banks, and, today, the lower Danube, save for its lowest extent, where it makes a sharp turn North, is the border between Romania and Bulgaria.
So, how did this state of affaris come to be? Why is the lower Danube a political and cultural border, unlike most major European rivers?
TL;DR: Your question asks “why is the lower Danube a political and cultural border?” I would partially dispute the premise of your question. In thinking about Central Europe in the early modern period, it is more important to conceive of the Danube River as a key pathway for troops, commerce, and communication than to think of it as a border. The entire Danube, from its headwaters near Vienna to its delta into the Black Sea, was a major “natural channel[] of intercourse and intermingling, of coalescence and union” (to quote Heilprin).
At the same time, you're somewhat right: the lower Danube River did form a porous border between the Ottoman Empire (in Greece and Bulgaria) and the Principality of Wallachia. To the extent that there was an open border along the lower Danube River between the Ottoman Empire and the Principality of Wallachia, the history of Wallachian rebellion and uneasy Ottoman occupation explains why such a border persisted.
Here is a map of the political divisions in Central Europe in 1590, which u/cyowari made brilliantly and posted on r/MapPorn. South of the Polish-Lithuanian Commonwealth and the Austrian hereditary lands, we've got Royal Hungary (light orange, underneath the “burg” in “Austrian Habsburgs”), the Ottoman Empire, the Principality of Transylvania, the Principality of Wallachia, and the Principality of Moldavia.
Here is a terrain map of the region. I have never been able to find a good map that includes both terrain features and key medieval cities, but not modern political boundaries and roads, so I bastardized this one in MS Paint. (Hey, I'm a historian, not a graphic designer.) You can immediately see how the terrain overlaps onto the political boundaries: the Habsburgs controlled everything to the eastern edge of the Alps (#7) and up through the Northern Carpathian Mountains (#8); the Ottomans controlled the Hungarian Plains (#9), the entire mountainous region of Serbia, Bulgaria, and Greece (south of #3-4-5), and the Balkan Mountains (#13-14); Transylvania existed on the Transylvanian Plateau (#10); and Wallachia on the Wallachian Plain (the flat land around #5-6).
Even before the Ottomans captured the Byzantine capital of Constantinople, they sailed from Anatolia (Turkey) up the western coast of the Black Sea and landed at the mouth of the Danube River (#12 on the terrain map). In the mid-1300s, the Ottomans conquered Wallachia (#5-6). In 1396, the Pope ordered a crusade from Europe to the city of Nicopolis (#5), which was the first major battle between a European coalition of Hungarians, Germans, Wallachians, and Poles versus the Ottoman Turks. It was a devastating Ottoman victory. In 1444, the Pope ordered another crusade to Varna, a city on the Black Sea coast at the base of the Balkan foothills (#13). The Ottomans won that battle too. In 1453, the Ottomans finally took Constantinople (#15) from the Byzantines. In 1521, the Ottomans were back in Central Europe and captured Belgrade (#4). In 1526, the Ottomans obliterated the Hungarian army at Mohács (#3) and killed the Hungarian king. In 1529, the Ottomans besieged Vienna (#1) for the first time, but the Christians were finally able to fend off the Ottomans and keep their capital. In 1541, the Ottomans took Buda and Pest (#2) instead.
You can clearly see that the Ottoman incursion into Central Europe directly followed the Danube River: the river was where all the important cities were, and both the Ottomans and the Germans used it as the main corridor of transport for troops between the 1350s and 1683. The Ottomans started at the Danube delta and proceeded directly along it from Varna → Nicopolis → Belgrade → Mohács → Buda/Pest → Vienna. The Habsburgs used it as a pathway in the opposite direction to move troops from Vienna → Buda and Pest → Mohács → Nicopolis. In that sense, The Nation was absolutely correct: the Danube River was not a border, it was a path of transport for Ottoman troops, commerce, and communication. Without the Danube River, the Ottomans would never have had a major “road” into Central Europe and perhaps they might never have punched as far onto the European continent as they did.
By 1520, the Hungarian and Wallachian peoples found themselves squeezed between three European superpowers: the Habsburg Empire centered in Vienna, the Polish-Lithuanian Commonwealth based in Kraków, and the Ottoman Turks stemming from Constantinople. To make matters even harder for the Hungarians and the Wallachians, much of their territory comprised flat, difficult-to-defend plains. As the relationships between the superpowers became increasingly tense, the superpowers fought for diplomatic and/or military control of Hungary, Transylvania, and Wallachia so that they could use these territories as buffer zones between them and the opposing power(s).
This dynamic squeezed Transylvania and Wallachia, but it also gave them one key bit of leverage: if the Habsburgs didn’t offer the principality enough military support/sufficient religious freedom/acceptably low taxes, the principality would simply flip its support to the Ottomans. If the Ottoman demands for tribute became too onerous, the principality would flip its affiliation back to Habsburg suzerainty. This dynamic completely characterized geopolitics in Central Europe between 1350 and 1683.
After the Ottomans first invaded Wallachia in the 1350s, the voivodes of Wallachia resisted the sultan with mixed success. In 1435, Wallachia had two competing voivodes: Alexander I Aldea, who had the support of the Ottoman sultan, and Alexander's brother, Vlad II Dracul, who had the patronage of the Holy Roman Emperor. In 1436, Vlad II Dracul seized Wallachia from his brother, but within a year the Holy Roman Emperor was dead and Vlad Dracul had to capitulate to the Ottomans. In 1441, Dracul betrayed the Ottomans when he and Transylvanian Voivode John Hunyadi liberated neighboring Transylvania from the Turks. The Ottoman sultan punished Dracul by confining him at Adrianople, demanding Wallachian tribute, and taking two sons as hostages. As a reward for Dracul's alliance, Hunyadi betrayed Dracul and installed Dracul's cousin as competing voivode of Wallachia. The Ottomans eventually released Dracul, but Hunyadi invaded Wallachia in 1447. Dracul fled Târgoviște and his own countrymen killed him.
After Wallachians assassinated Vlad II Dracul in 1447, the Ottomans placed one of their hostages, Vlad III Dracula, on the throne. Dracula fought Hunyadi with Ottoman support, but had to flee to the Ottomans between 1449 and 1456. He finally came to power in Wallachia in 1456, whereupon he immediately purged all the boyars who had supported Hunyadi/conspired against his father. His mass execution of the boyars by impalement inspired his reputation for astonishing cruelty that we know today.
A century later in 1593, the Ottoman Turks installed another famous Wallachian prince, Michael the Brave. As soon as Michael's predecessor did not play well with his Ottoman administrators, the Ottomans exiled the predecessor to Constantinople (where they strangled him to death) and enthroned Michael. But Michael came to power at a tenuous time: the uneasy peace between the Hungarians and the Ottomans started to devolve into outright conflict, and the pope called for a new Holy League of Italians, Germans, Hungarians, and Poles to invade the Ottomans. Although Michael only came to power with the help of the sultan, he quickly betrayed the Ottomans and joined the Holy League. He was a brilliant military commander: he retook the biggest Ottoman cities in Wallachia: Nicopolis, site of the failed crusade in 1396; Bucharest; the Wallachian princely capital at Târgoviște; Giurgiu; and Adrianople, a major Turkish city (today, Edirne). Just 5 years after Michael allied with Transylvania in the Holy League, however, he betrayed that ally too. He invaded and conquered Transylvania, but he only ruled until 1600. One year later, the Habsburg emperor, an ally of Michael’s, betrayed Michael and assassinated him.
The examples above are only a few of the many Wallachian rebellions against the Ottomans. The important takeaway is that Wallachia was, as you say, an Ottoman tributary, but it was a particularly cantankerous one. The Wallachians were able to resist full Ottoman assimilation for centuries because they could always seek support from the Germans or the Poles against the Ottomans. And when German patronage became too oppressive, the Wallachian prince could simply flip his support back to the Ottomans. To the extent that there was a porous border along the lower Danube River between the Ottoman Empire and the Principality of Wallachia, the history of Wallachian rebellion and uneasy Ottoman occupation explains why such a border persisted.