Starlink would have to comply with what the country they are transmitting to permits or doesn't if they don't want to get in all sorts of trouble. An effect that Starlink could have though, is, that people might protest censorship more because all that stands between them and freely accessing the internet is their government allowing import of receivers (instead of no cable or mobile available at all, ISPs, government, ...).

That's incorrect. They will need permission from countries to transmit to its areas.

Until they either get jammed or shot out of the sky

That and people using the service, even solely receiving can be tracked