One of the consequences of the Sputnik launch was that it basically enshrined the principle that overflying another country with an active satellite was not an illegal act. (That is, the US government decided not to protest, because it meant they wouldn't have to apologize for their own future spy satellites.) I doubt China wants to break this precedent.

This thread applies also to Russia, where complaints about coming constellation were already voiced in the government.

In both cases I assume the issue at stake is the freedom of communications. I'd hope to have both technical means to communicate (and hide those communications) and enough support on USA side not to pressure SpaceX to deny service worldwide.

We'll see how it goes.