Overall, yes it is a coincidence. If you compare English to other Germanic languages, you run into the issue of English's extensive vocabulary of French and Latin origin, as well as its general lack of mutual intelligibility with German and Dutch (both of which maintain a small level of mutual intelligibility). German and Dutch, as well as English, have minimal mutual intelligibility with Danish/Norwegian/Swedish, three nations which became heavily protestant, and have almost none (if any) with Finno-Ugric Finnish. There is also the issue of whether it is fair to define Anglicanism as Protestantism at all, given it has a completely different origin than the other (Protestantism, in a general sense, arises out of the teachings of Martin Luther and John Calvin. Anglicanism is a result of the marital escapades of King Henry VIII and Queen Elizabeth I's codification of the new Church of England).

Even within the German and Dutch speaking world, there is no clear hegemony of Protestantism or Catholicism. Catholicism remained the dominant faith in the southern Dutch-speaking areas (which would later become Belgium), and remained a prominent force in the northern areas (the modern Netherlands). Even up until the 1970's, Catholicism made up some 40%-ish of the population of the Netherlands.

Germany itself, in the relevant time period the Holy Roman Empire, a loose grouping of dozens of independent duchies, a kingdom (Bohemia), archbishoprics, an archduchy (Austria), free cities, and other such entities, was divided between Catholicism and Protestantism. While in the northern states Protestantism quickly became the dominant faith, states like Bavaria and Austria remained Catholic, and others, such as Bohemia (which will be discussed more later) flip flopped between the two.

Even within the Romance-language speaking world, there was initially a great deal of Protestant ideology and Protestants flying about. In France, the Protestant group called the Huguenots became a prominent force, though they were persecuted and eventually forced out of the nation, fleeing to places like England and the New World (for example the Carolina colony, where the Huguenots formed a serious political block in the city of Charlestown (now Charleston)). In Italy, the most notable Protestant denomination was (and is today) the Waldensians, a group which actual pre-dates Luther by several centuries, though they later grew closer to the churches that spawned from the ideas of Calvin. The Waldensians, however, have never been a very large group, and the Catholic Church remained, unquestionably, the dominant faith. This dominance was ensured within Italy's disparate states and within the Spanish and Portuguese realms (two nations which experienced little in the way of conversions to Protestant denominations) by and large through the efforts of the Inquisition as well as their respective governments' general intolerance towards Protestant ideology.

As mentioned earlier, there are other linguistic groups at play in the division of Europe between Protestant and Catholic adherents. Three of these languages are not, in fact, actually related to the others at all: Hungarian, Finnish, and Estonian. All three of these are Finno-Ugric languages. By and large, these are split today between Catholicism and Protestantism, but this was not always the case. In Hungary (which still has a sizeable Protestant minority), Catholicism is today the largest faith, but initially after the introduction of Protestantism into the world, Hungarians by and large converted to Protestantism. It was not until the second half of the 16th century that, through the efforts of the Counterreformation and the Jesuit order that the Hungarian populace returned to the Catholic faith. Finland is slightly more complex, given an Orthodox minority that developed under Russian rule, however the vast majority of Finns were members of the Church of Sweden (later breaking off their own church, the Church of Finland in 1809), a Lutheran church. Likewise, in Norway and Denmark there are the Church of Denmark and the Church of Norway, both Lutheran, as well as in Iceland, the Church of Iceland. Estonia, the almost forgotten Finno-Ugric language here, was almost entirely Lutheran before the Soviet occupation, and is today mostly irreligious, Orthodox (some 16%), or Lutheran (nearly 10%).

Another group of languages (this one actually related to Germanic and Romance languages) is that of the Slavic languages, which bears its own history as regards Protestantism and Catholicism. Poland, speaking Polish (duh), is almost entirely, and historically has been almost entirely, Catholic. It does, however, have a few regions, such as parts of Silesia (Śląsk/Slezsko/Ślůnsk) that are historically Protestant, however, numerically speaking, this portion of the population is mostly insignificant. Like in Estonia, the Orthodox church holds more sway than any Protestant group (though both Orthodoxy and Protestantism are wildly overwhelmed by Catholicism, unlike Estonia). In Bohemia (the modern-day Czech Republic), Catholicism has a bit of a rough history. Before Luther, there was Jan Hus, who accidentally created his own denomination of Christianity after getting burnt at the stake. These are called the Hussites, and their sudden dominance in Bohemia (but notably never really over the region of Moravia) caused great concern across Europe, and resulted in twenty years of war between Bohemia (with the help of Poland and Lithuania) and the Catholic world, called the Hussite Wars, and actually resulted in a Hussite victory. The Hussites later adopted ideas from Luther and Calvin, and would play an important role in the early stages of the Thirty Years War (which they may have sort of kicked off). After the Thirty Years War, the Hussites were defeated at the Battle of White Mountain, and the re-Catholicisation of Bohemia began (Notably, this defeat, which happened in 1620, ended two centuries of Hussite rule in Bohemia). By 1781, so few Hussites existed that the movement did not even experience much of a revival under Emperor Joseph II. This changed when the Austro-Hungarian Empire dissolved after WWI, and the Catholic Church became seen as a symbol of Austrian rule. There was a mass movement in the Czech regions of Czechoslovakia to convert to revived Hussite churches, resulting in a majority Hussite nation. This movement died after WWII and the introduction of Communist rule, which oppressed religion of all kinds. Today, like Estonia, Czechs are mostly irreligious. However, there is a large Catholic minority, though this is shrinking. Slovakia remains Catholic as well.

So, ultimately, the divide between Protestant and Catholic is really more geographic, and ignores the divides within Protestantism and the questionable place of Anglicanism within Protestantism (as well as the presence of the Orthodox church). It is merely coincidence that Germanic languages occupy a good deal of the same area as Protestantism, and, as demonstrated, it is not just to speakers of Germanic languages that Protestantism appealed or converted, and likewise under no circumstances did just Romance-language speakers remain Catholic.

Also, I forgot Croatia and Slovenia. Sorry, Croatia. Croatia, another primarily Slavic-language nation, as well as Slovenia, remained primarily Catholic, being part of Hungary and Austria respectively through most of the relevant time periods.

As a partial add on could these divisions be linked back to the boundaries between Arian and Nicene Christians?