One must also remember the west was hardly a Utopia for LGBT rights until a decade or two ago and to this day huge swaths of the US are filled with evangelical fanatics.
Let's start with women. They're roughly half the population. If they are being systematically mistreated, that's a much, MUCH higher percentage than are affected by Catholic priests, Timothy McVeigh, and the Mormons.
Also, the mistreatment of women is in most cases baked into the laws in "the Muslim world." Christian pedophilia, as widespread and terrible as it is, is still illegal. (Yes, Trump II may change that.)
I'm hardly an apologist for the excesses of the West, and Christianity and Islam are both "religions of the book." The difference is that Christianity has evolved through a process of liberalization, and most Western countries aren't literally ruled by "the book" in the way that "the Muslim world" is. (Yes, Alito and Coney Barrett want to change that.)
I think you're just arguing or the sake of arguing. Within two SDs of the mean income, I doubt there's a person alive - and definitely not a woman or gay person! - who would rather live in "the Muslim world" than in the West. And that's a terrible shame, but it's also self-inflicted harm by most of those countries.