> How would a nation state block access?

Make it illegal to enter your country with an unauthorized receiver like India does for Iridium and various satellite phone services.

Make a deal with the network and make it mandatory to use a local service provider or register SIM cards for visitors like Russia does for Iridium.

I'm sure you can just jam their signal. It's very easy to overpower a distant signal from space with a nearby transmitter and ground-based power.

That would require transmitters placed across the whole nation though, right?

Yes, these are phased array antennas on the ground so they can point right to the satellite as it passes overhead and ignore almost entirely everything nearby. By happenstance, this design also helps with reducing sidelobes on transmit and receive, the easiest ways that a third party could jam and detect this terminals. Unfortunately, this first generation of Starlink birds do not have intersatellite links meaning they still need a ground station somewhat nearby to provide the other end of the comm link. Even if you did sneak a terminal into a country, there wouldn't be any terminals nearby providing the internet connection anyway. One SpaceX figures out how to get the laser intersatellite link going, this will be a very lucrative business.

I'm not exactly sure what the best use of this current generation of Starlink is, I guess it could provide backbone for rural cell towers. It sounds like it's totally useless for aircraft and ships out in the ocean (major Iridium customers) and too expensive for individual rural residential users. I'm sure it would be possible to setup small Starlink-based ISPs in rural areas that could use dark fiber lines or microwave links to provide internet for rural users.