What we've seen of Chinese heroes in the comic book continuity (Radioactive Man, Collective Man, 'China Force') suggests that mutants or superhumans born in China tend to be drafted into the army / government service.
More info on that
here.
How that applies (or if it would be relevant at all) to the cinematic universe remains to be seen.
We don't really know what they've got access to in the way of ultra technology or 'omega level' mutants, but given the nature of their government, very authoritarian and willing to make large decisions without fear of any sort of oversight or checks and balances getting in their way, if they *did* have access to Stark level tech or mutants with massively society-affecting powers like telepathy or weather control, most likely those sorts of things would result in some pretty huge changes. (So, to keep 616 China as similar to 'our' China, it might be best to assume that they *don't* have a Stark, or a Storm, or a Xavier, since, unlike the more fractious and adversarial US political environment, where any proposal, no matter it's benefits, will automatically be opposed by the rival party for purely political purposes, China might more rapidly embrace some pretty shocking changes.)
I don't think the existence of Thor, or even ancient Chinese deities walking the Earth (at least 14 of which are already established as existing in the 616 universe), would much affect Buddhism, which (as I understand it, anyway) is more about the advancement of the self than worshipping external beings.