I went to a gay Muslim wedding a few years back.

I hate to break it to you, but there's no such thing as a gay muslim. The religion is pretty explicit about homosexuality not being accepted. If you're gay then muslims don't view you as one of their own if you claim you are one. The polls pretty heavily back this notion.

Blaming religion for making people assholes robs them of their agency, letting them off the hook for being assholes organically and allowing the institution to shoulder the blame.

They're not being assholes organically. They hate gays because their religions instructs them to hate gays. Your ignorance on islam doesn't change the fact that islam is what drove these parasites to beat up these girls. Homophobia in islam runs really deep. The faster we address, the less of these instances we'll have in the future. The more you rush to defend islam, the more people will end up being victims of such attacks.