China is a one-party psuedo-communist state, which is ultra far-left - the polar opposite of political conservatism. Yes, gay marriage is not permitted, but thats due to social conservatism.

You're correct in saying China is socially conservative, but saying its conservative implies a right-wing political ideology. It lacks nuance and implies something that is factually wrong.

Russia - yes very conservstive. Soviet Union was politically far-left but modern Russia is basically christo-fascist. So its culturally, politically and religiously conservative.

You're framing it in the American context though. Mixing politics and religion is taboo in most western democracies. And, religious conservatism isn't the same as political conservatism.

Ireland is a good example - devoutly Catholic but with very liberal politics. Gay marriage has broad support.

UK - pretty much godless and very liberal - but historically politics has been dominated by the Conservative party. Broad support for same-sex marriage, and it was actually brought in by a Conservative government.

China - authoritarian single-party system. Follows Communist ideology with a capitalist bent. Religion - taboo, government controlled, doesn't feature in politics at all. The important difference is that its culturally very Asian. Even eastern democracies like South Korea and Japan have a tricky relationship with gay rights.

If that were to change you'd imagine CCP would support gay marriage as it poses no threat to ideology or party policies.