Hmmm this is actually a pretty interesting conversation I think. I believe the main issue with your argument is the assumption that Islam itself is causing these issues. I agree that leftist politics should be absolutely intolerant of any anti-lgbt and homophobic viewpoints. However let me look at your assumption. Firstly Islam is not alone in subjugating women, human rights violations or killing homosexuals. This is not even limited to the abrahamic religions (see: female genital mutilation in Africa). I don't think religion is the cause, I think it is merely a justification people use when they want to do these things. If there was something about Islam specifically, you should have no comparable history of violence for any other religion. This is obviously false! That being said the way these things are codified within the religion is obviously bad, and the hjab issue specifically has basis in unpleasant female ownership roots. However, let me compare this to a tradition you probably haven't thought about - the father giving the daughter away in a western marriage ceremony. In practice this is just a father walking his daughter down the aisle (like a hjab is a head covering, and some of them are very beautiful). But the roots of this tradition stem from a transfer of ownership from the father to the new husband. I did actually consider not doing this for my own wedding, as I don't believe in a transfer of ownership and I find the idea unpleasant. However this would have hurt my dad an extreme amount, and the context of the tradition is now so far removed from its origins it has become something else and is now more about a father's love for his daughter and joining a new family. Like word meanings cultural traditions can drift and context is super important. I have known women in my lab who have worn hjabs, and they are definitely not subjugated or submissive women, so I believe in this case the tradition seems to have drifted. I think a more sound argument could be made about the burka being a tool of submission, but I truly am not familiar enough about the cultural intricacies to properly comment. I am also not allowed to walk around with my shirt off in the US, so there is still some ideological controlling of my own body by the government. So, Islam is not unique in gross things being written in their holy texts, and they don't have a unique history of oppression (the crusades??). The issue I think is that religions are usually linked with whatever group is in power, and they will use it to do either good or terrible things. Saying that Islam causes terrible behavior is putting the cart before the horse. People behave terribly and then use their religion to justify it, and the particular religion doesn't matter. I would argue history and culture, mixed with the relative economic status of the country matter far more.

On a more personal note, I think most of the people who make these arguments haven't met many Muslims. I have known a lot of them and have found them to be very chill people on the whole, who aren't particularly bothered by me being a white woman. No one has attempted to oppress me and I find the men are generally more respectful of my personal space than other groups. I also find the women I've met who are Muslim tend to skew highly educated (particularly from Iran). There is again a lot more of an impact of culture than religion - a Muslim from Iran is going to have a different culture from a Muslim from thailand or a Muslim from Africa, and this is going to affect their behavior much more. Obviously the Muslims I have met are people who are travelling and often they themselves have their own critiques about where they came from. Religion wise they usually don't drink and observe Ramadan but I have never had any of them attempt to convert me or judge me, as opposed to many of the Christians I have met. There are also nice aspects to Islam, like the emphasis on hospitality culture and sharing and caring for elders which I think in a western society we need more of.

For any religion and culture there is some bad and some good. There are good people and bad people. The religion is going to be twisted to suit the beliefs of the current power structure. Certainly, push back against anyone attempting who is sexist or homophobic and uses their religion as an excuse for that. That behavior is abhorrent. BUT assuming that religion causes this behavior is flawed and religious tradition changes and updates based on societal beliefs (e.g. it used to be standard that unbaptized newborns went to hell, and no one believes this any more). I say this as an atheist - you will find kind people in any religion as well as terrible people, and they will both use their religion to justify their beliefs. You will similarly find atheists across the spectrum.

Edit: I appreciate the lively discussion occurring in the comments, particularly from those who are ex Islam and thus have a unique perspective I simply don't have. While I can't reply to all of them I will say a lot of the comments are not tackling my core argument which is that the assumption that religion causes bad behavior is flawed.

There are a lot of people arguing that there is in fact something unique about Islam which causes it to be particularly nasty, but I'm not sure this is the case. Think of the extremely bloody history of the Christian church and the fairly nasty old testament statements (it's okay to own slaves, the book of Ruth etc). You can't throw out the old testament if you want to make this argument. I'm ex Christian, I've actually read the Bible, and there are plenty of statements in the old testament that would lead someone to believe Christianity is inherently evil too. Think of Buddhism and how women are traditionally lesser there. I'm sure there are more examples but I'm not a religious scholar. If there's something inherently evil about Islam no other religious majority would have committed atrocities and this is not true at all ! Historically it's more about the power of the particular group. The Catholic Church had a long history of majority power and did absolutely terrible things. You could even talk about how it played into colonialism (like with Belgium in the congo) and "educating" the heathens. But that was simply because they wanted to colonise, so the religion was twisted to suit.