If every country with an economy the size of 1 or 2 large US states start making up their own censorship laws and trying to force companies to enforce them, at some point this causes huge inefficiencies.
I can see two end states to this:
1. If the censoring country has enough international legal influence, companies will probably have to block users from that country from using their services.
2. If the censoring country does not have enough international legal influence, the company ignores them and the government has to explicitly censor its citizens' internet connections.
I kind of prefer the second because it's more visible and dramatic - I think a lot of people probably aren't even aware when their country has censorship laws.
This also creates economic opportunities for two classes of alternative content distribution:
1. Content distribution based out of legally friendly countries, a la the Sultanate of Kinakuta. Expect to see the media start using terms styled after "tax haven", like "cybercrime haven", for countries that don't enforce US/EU censorship/copyright laws.
2. Content distribution based off of peer-to-peer networks that are harder to wage lawfare against. Bittorrent, IPFS, etc. fit the bill here.