To start off with, I would suggest taking a look at a couple of previous answers by u/sunagainstgold:

Comic about gender identity during the Middle Ages (and among Catholic priests in particular) got to the FP of Imgur. How true is it?

and

I'm a male peasant in 13th century England, and another villager catches me and my male friend having "relations". How likely is it we'll be executed for sodomy (or anything else)?

Basically the short answer is no, no one was really "homophobic" yet. No crusaders (or anyone else) would have gone around looking for homosexuals to persecute or kill, because they also hadn't really invented the categories of heterosexual and homosexual yet.

(But really, read sunagainstgold's posts, she's explained it much better than me!)

That being said, sometimes the issue of improper sexual relations (which we might or might not categorize as "homosexual" today) did come up during the First Crusade and afterwards. Sometimes if the crusade was going badly, the chroniclers (who were almost always priests) attributed it to the crusaders' sins; this could include "fornication", "licentiousness", "unrestrained lust", whatever they meant by that. For the most part they're probably talking about prostitution - there were always prostitutes following crusader armies, not just on the First Crusade.

Sometimes their sexual sins include visiting male prostitutes though, especially in Constantinople - chroniclers of the crusade loved complaining about the looser morals and effeminate ways of the Byzantine Greeks:

"Finally reverence for all that was called Christian was handed over to the brothel. When the female sex was not spared (an action which might be excused since it is at least in accord with nature), they became worse than animals, breaking all human laws by turning on men. Their lust overflowed to the point that the execrable and profoundly intolerable crime of sodomy, which they committed against men of middle or low station, they also committed against a certain bishop, killing him. " (Guibert of Nogent, pg. 37)

Guibert of Nogent wasn't actually present on the crusade, and is well-known for his hatred and disgust of, well, not just sex, but pretty much everything else in life, so we probably can't take him literally. But this is a pretty good indication of religious attitudes to sex - it wasn't homosexual sex specifically that was the problem, but homosexual sex was among the various illicit kinds of sex.

In this case Guibert mentions that sodomy is not "in accord with nature", which means that it can't lead to procreation. Here he happens to be talking about homosexuality (or at least men who have sex with men, in modern terms), but sodomy could also include any other kind of non-procreative sex, even with women.

The First Crusade ended up being a success, and the chroniclers often attribute this to sex-based reforms like expelling prostitutes or avoiding lust in some other way. But sexual impurity was still a concern in the early years of the crusader Kingdom of Jerusalem.

In 1119, the crusaders were defeated near Antioch at the Battle of Ager Sanguinis ("the field of blood"). Once again they assumed they had lost God's favour due to their sins, sexual or otherwise. So in 1120 they established a rudimentary legal code, which was meant to raise moral standards and, consequently, regain divine favour. The code is known as the "canons of Nablus" and among other things, it forbids sexual relations between crusaders and their Muslim slaves, bigamy and adultery between married crusaders, and, again, sodomy.

This time sodomy always seems to mean sex between two men, but there are different outcomes depending on the ages of each party. Adult "sodomites" would both be burned at the stake, but if one party was younger (possibly but not necessarily a child), only the adult would be burned.

So, there wasn't really such a thing as "homophobia" yet and it's hard to say that there was even such a concept as "homosexuality". There were only different kinds of sinful sex, one of which was "unnatural" sex, which could include (but was not limited to) sex between men. Despite that, they clearly did distinguish between sodomy between men and women and sodomy between two men. The latter was a more serious crime that could be punished by burning at the stake.

Sources:

James A. Brundage, "Prostitution, miscegenation and sexual purity in the First Crusade", in Crusade and Settlement, ed. Peter W. Edbury (University College Cardiff Press, 1985)

Benjamin Z. Kedar, "On the origins of the earliest laws of Frankish Jerusalem: The canons of the Council of Nablus, 1120", in Speculum 74 (1999)

Guibert of Nogent, The Deeds of God Through the Franks, trans. Robert Levine (Boydell, 1997)