They don't care if it's an Islamic republic unless it goes against their imperial interests. I don't hear them sparking color revolutions and uprisings, or even trying to invent reality for interventions in Dohran, Dubai, Riyadh etc.
The "Islam repressive to women and queers" shit is a "rules for thee and not for me". The US and its allies are the ones oppressing minorities, trans, queers, woman, and the rest of their non-white straight cis male population in their countries, as well as abroad.
Don't get me wrong, I'm not saying Iran, Hezbollah, Hamas, and Ansarallah (Houthis) are all progressive and accepting, but most of the claims regarding this topic are straight-up wrong or overexaggerated, particularly the topic of Women, Iran, and Hezbollah, especially during and after Sayed Hassan Nasrallah's (may he rest in peace) reforms . Not too knowledgeable about Ansarallah and Hamas's positions on this to talk about them.
Most if not all countries where gay and women's rights are lacking are a direct result of British and French colonialism. Before that, being queer or trans was in between the spectrum of celebrated, accepted, or frowned upon. It is the colonizers' barbaric white supremacist culture that brought the rights issues of today that they point towards as a justification for their intervention, colonization, and imperialism.