There is virtually no physical legacy of the crusades in the modern Middle East.

I suppose it depends on how you define “significant”, but immigration to the crusader states wasn’t too similar to early modern colonization in Africa, the Americas, and later Australia. Partly this was because they just hadn’t invented that concept of colonization yet in the Middle Ages. They weren’t invading unknown or newly-discovered lands. The Near East was already part of the ancient conception of the world and the crusaders believed they were simply restoring it to its proper rulers. It wasn’t a “no man’s land” open for settlement. Secondly, for the most part they also hadn’t invented the concept of a centralized nation-state yet, so there was no way to organize emigration and colonization on a massive scale.

Historians have tried to determine the population of the crusader states and the relative numbers of native inhabitants and European immigrants, but we really have very little idea of the numbers involved here. Josiah Russell calculated that all of Syria had about 2.3 million people at the time of the crusades, living in perhaps eleven thousand villages, although of course most of these people would have been outside of crusader rule. The population of the Kingdom of Jerusalem specifically has been estimated at 360,000 non-Franks, most of whom (about 250,000) lived in rural villagers. For the crusaders (“Franks” or “Latins”), there may have been between 100,000 and 140,000, or 15 to 25% of the total population, depending on how big the overall population is supposed to have been.

On the other hand it’s possible that these numbers are wildly overinflated. The Franks themselves, at least, believed that they were a very small ruling class among a much larger population, and that they were mostly confined to a few cities and castles in the interior. Surely a figure of 25% of the population would be a much larger number of people? The problems with figuring out who lived there are summarized by Ronnie Ellenblum:

“Not only do we not have any information about the size of the Latin population, but all other demographic factors are also unknown to us. We do not know the size of the whole population, what their age and sex distribution was, how many children a fertile mother might produce, the average life expectancy, the average marriage age, the death rate amongst children, the rate of death from illnesses and plagues, and other demographic details. Furthermore, the figures, of dubious veracity, given for the inhabitants of the large cities, include an unknown number of local Christians. The questionable measure of the size of the population of the large cities is based for the most part on descriptions of war and siege during which the rural population in the vicinity were also concentrated in the cities. The numbers given in contemporary historical sources are often grossly exaggerated and do not distinguish between the Franks and the local Christians. In such circumstances a real demographic study becomes only wishful thinking.” (Ellenblum, pg. 30-31)

Ellenblum believes the Frankish population was much smaller than 25% or even 15%. His book is actually about settlement patterns, which is not entirely relevant here (although pretty fascinating if you’re into that sort of thing; he argues that the small number of Frankish immigrants settled in cities, but also in rural areas where native Christians already lived).

The reason I bring this up is because it’s probably wrong to think that there was “significant” immigration to the crusader states. Hardly any of the crusaders who came there from Europe stayed there. They mostly went back home. Those that did stay were only there for less than 200 years; the crusader states on the mainland were all destroyed by 1291. The European population either fled back home, or they were killed or enslaved. There were no European Christians there at all after 1291 until the 15th century, and then the ones that settled there after that were mostly monks and priests.

There is a bit of a material legacy. There are some ruins of crusader villages and churches. The Church of the Holy Sepulchre in Jerusalem and the Church of the Nativity in Bethlehem were rebuilt by the crusaders, so you can still see elements of European Romanesque/Gothic architecture. Some crusader castles still exist, such as the massive Krak des Chevaliers (recently damaged during the civil war in Syria).

There is also one religious legacy - the Maronites of Lebanon united with the Latin Catholic church during the crusades, and they are still in communion with Rome today.

There might also be some “legacy” in terms of genetics, but it’s not very clear. There have been some genetic studies, but unfortunately, historians typically don’t really understand or use scientific studies, and scientists likewise don’t really understand historical sources, so there’s little coordination between the two (or none at all).

During the two centuries of the crusader states, there definitely was some intermarriage between European and native Christians, and probably also with converted Muslims (maybe along with a bit of sexual abuse of enslaved Muslims). So it's possible that there's some kind of modern genetic admixture. I know that anecdotally, people from the Near East sometimes believe they have European ancestry. A Palestinian friend of mine tells me that green and blue eyes are a trait in his family, and “everyone knows” it’s a European crusader trait. I’m not sure how likely that it is but it’s something people believe, at least!

The genetic studies I was able to find actually suggest that there is very little trace of European genetic markers in the Near East. One study looked at people from different religious groups in Lebanon (the aforementioned Maronites, as well as Greek Orthodox, Muslims, and Druze) and concluded that they were all genetically very similar with no significant differences. Any genetic differences actually seem to go back even further than the existence of Islam or Christianity. Presumably, the ancient population of Lebanon converted to Christianity, and then later, Muslim settlers in Lebanon largely came from further south in Arabia. Later there was some mixture with crusaders from Europe, and later still, there was another wave of immigration from the north when Lebanon was part of the Ottoman Empire. But only the initial Muslim conquest and the Ottoman period seem to have had any significant effect on genes.

So in summary, there is zero legacy in terms of political boundaries or institutions, but the crusaders did leave behind a bit of material legacy in the form of churches, castles, and ruins of villages and other buildings. Since there were so few of them, their legacy among the genetics of the modern population is probably insignificant, although that question goes a bit beyond the competence of historians and not much research has been done on that.