If SpaceX wants to deploy in China, it will be on China's terms. I think that Tesla's chinese factory doesn't greatly change that. SpaceX will get permission to sell to users in China only if the Chinese leadership thinks it's in China's and their interests.
If China wants access to the US market for Hongyan, SpaceX and the FCC might be able to negotiate some form of access for Starlink to the Chinese market. Likely this would involve access from China relayed through Chinese ground gateways.
China especially heavily leverages their infrastructure for geopolitical purposes. Censoring and monitoring inside the country, launching attacks outside of the country, etc. I really doubt they want the US to get any leverage in the form of controlling some of the nodes, even if they are supposed to by agreement only route traffic from inside China to inside China.
Starlink doesn't mean that magically Russia, Cuba, and North Korea are all going to have unfettered internet access.