Carole Hillenbrand (in The Crusades: Islamic Perspectives, her marquee book on Muslim views on the Franks and the Crusading period) described the Muslim view of the Franks as being "dirty, deceitful and lacking in marital jealousy, and of Frankish women as sexually loose." Basically, they considered them to be barbarous and unsophisticated.

I can't speak to the question of homosexuality, but some Muslim writers certainly saw the Ifranj (Franks) as being unsuitably lax in terms of their protection of women's virtue. A great example of this is an episode from Usama ibn Minqidh's Kitab al-I'tibar, which I've talked about in another answer in this subreddit. He wrote that a Frankish man was amazed by how he (Usama) had shaved his body hair when they encountered each other in the bathhouse (hammam) and asked to be shaved in the same way. The hammam was a common social space in the Islamic world, building off of Roman bathing traditions. While they were public sites, they were strictly gendered. Except in this story, the Frank brings his own wife in to be shaved like he had just been. To be clear, the fashion was for men to be basically entirely shaved below the neck, including the pubic hair.

We should ask ourselves a couple of questions about what this anecdote means. Is it a case of a factual encounter between Usama ibn Munqidh and his Frankish neighbours? His life passed almost entirely between the years of Frankish control of Jerusalem, and his work is famous for its descriptions of pretty friendly relations with the Franks. With that said, he also spends plenty of time cursing the Christians, too! It's always possible that Usama ibn Munqidh encountered a quite unusual knight in the hammam who for whatever reason had no problem with bringing his wife into a male space to have her pubic hair shaved. But I think it's a lot more likely that the story is exaggerated. His audience was predominantly Muslim Arabic-readers, who would have been as likely to disdain the presence of the Latin Christians in the region as much as he did. Many of his stories portray the Franks as being kind of buffoonish, socially illiterate folks-- clowns. As you can see, at least in this case, Hillenbrand's assessment of the Muslim view of Latin Christians is pretty accurate.

In my own interpretation, while there are certain commonalities between Latin and Muslim views of each other, the Muslim stereotype about the Latins has a different character. They aren't engaging in these behaviours because they're depraved, blasphemous schemers. To make connections to modern racist stereotypes, the Latin view of Muslims had more in common with twentieth century images of "Chinatown" as a den of sin with scheming Eastern men that White women needed to be protected against, while the Muslim view of Western Christians was more in line with the Western view of Black people as being primitive and therefore lacking in sophistication. Hillenbrand points to the idea that Islam superseded Christianity as a reason for Muslim high-mindedness toward the Franks, and I think that might hold true in this case as well. They viewed themselves as being part of a more advanced form of society because of their more advanced religion.