I think they might be coloring with a bit of a broad brush, but religion - broadly speaking - is conservative. Some religions may promote values that we agree with and traditionally associate with progressivism (pacifism, egalitarianism, altruism). It’s because they’re based primarily on old or even ancient writings.

I was raised a traditionalist Catholic. I went to catholic school until high school until I went to high school where I became an atheist (which I didn’t even know was an option) and was invited by the school to investigate other educational opportunities.

I also studied Theravada Buddhism for many years. Theravada Buddhism isn’t conservative in the MAGA sense of the word, of course. Especially in the tradition I studied, it concentrates on personal investigation rather than treating the texts and teachings as literally true. A common way of presenting teachings is to say something along the lines of “If it helps, let it help. If not, ignore it.” Still, monks are not permitted (generally speaking) to interact much with women, monks and nuns live separately, and I honestly have no idea how a trans person would fare in that environment.

There’s always a problem when you found the basis of your philosophy in a historical text rather than a constantly evolving understanding. One of Chomsky’s chief complaints about Marxism is that it’s founded on and bound by Marx. He points out correctly that people don’t call evolutionary biology “Darwinism”. I mean, creationists do, and biologists might if they’re referring to a very specific concept, but for 99% of the time we just call it “biology.”

So, building your worldview around a fixed text is by definition conservative. Being flexible about its interpretation can make it less conservative. By and large, though, they’re trying to conserve something.