Modern historians typically say that the effect of the Crusades through cultural exchange was really quite limited. It is certainly true that the 12th century was affected by an increase in European access to classical scholarship that had been preserved by the Muslims but lost to Europe. However, scholars no longer believe that this came about through the Crusades. Instead, they argue that the cultural exchange happened by way of Spain. Muslims ruled all or part of Spain until 1492 and the cultural exchange there (as well as in Sicily) was much more intense than in the Holy Land where the Crusades were.
Nowadays, scholars say things like "There may have been some broadening of perspective" from the cultural exchanges but that it is "debatable" as to whether the Crusades had much effect on Europe (Source: Spielvogel,Western Civilization, 7th edition p. 300).