I don't think (western Christian) religious conservatives ever supported the fatwa against Rushdie? If anything they'd've been using it to argue about the barbarity and godlessness of Islam or something. The only people who would support murdering an author for blaspheming would have been "cultural relativism" lefties, and at the time it was issued the mainstream of those people, and those commenting in print, could still pass as rational. They hadn't gone off the social media/pomo/critical theory deep end yet.

We weren't talking about support for the fatwa. We were talking about people who believe certain things shouldn't be written or published, because they don't personally like them or find them offensive, whether for religious beliefs or other reasons.

Look at all the attempts to ban books over the years, and the majority of them (though not all) tend to come from those on the right and/or religious conservatives. It's never been limited to one side of the political spectrum though, and there are more people who describe themselves as left or liberal are joining in. They just tend to have different reasons to try to ban books and use different approaches than those on the right.