I work with middle eastern guys who are like this, they hide this side of themselves when I'm around (white guy) but it comes out when my female coworkers are alone. It's common enough that I've heard about it from multiple people. But when I'm around they're great and I consider them good work friends.
It's hard facing this as a lefty. I met a Muslim European colleague at an all hands in tel aviv during pride a few years ago. Went for super late night constitutional with a few other internationals including fellow Americans and the whole city was alive and really queer. In depth conversation with this otherwise really nice guy about how he would minimum believe mental illness, maybe disown, his daughters for being gay or trans. I understood it's religion like anti abortion and I'll never persuade him and didn't argue, just shared perspectives and asked questions.
It's not hard at all to face this as a leftist. You can acknowledge that homophobia and sexism are deeply rooted in Islamic religions while also recognizing that not every adherent is guilty of either. Pretending something isn't true because it's not pretty doesn't benefit anyone except those who would utilize the blind eye to continue to do harm to society.
Criminals can be victims, victims can be criminals. There is no rule that groups humans into two groups. Oppressed and oppressor with zero movement between the groups. Instead humans just go around, get hit, and hit. Sometimes they avoid hurting people because they can't, sometimes it is because they won't.
I have zero problems understanding that some Muslims have been mistreated by the West is one fact and a totally seperate fact is some Muslims would honor kill a LGBT person. Seperate facts.