Government cannot exactly "bar" terms of service. ToS isn't law. The most they can do is say they're unwilling to enforce them.

ToS is just conditions that you agree to in order to use a private service that is provided at-will. I can have a private coffee shop where the terms of service are that you must wear red to enter, and if you're not wearing red, you are not welcome on my property.

So it would be upto OpenAI and Anthropic to enforce them on their own terms (by banning accounts and IPs).

The government absolutely can pass laws that ban particular contract previsions. They do that all the time. In your analogy for example while they can require you to wear red, they can't require you to be white.

Governments can do anything they want by passing a new legislation. In your example, they could easily pass a law that states that any ToS cannot reject service to a customer based on the color of their attire. In the USA, it's obviously already illegal for a business to reject service to a customer based on some protected classes like race.

That's just not true. You can absolutely have terms of service that are illegal, and the government can enforce them.