How large is the set of things that Western European governments would be OK with, but the U.S. government wouldn't?

Nothing significant: Western Europe is run by the state department, and less directly, by Harvard through the London School of Economics.

Eastern Europe, however, not so much. Estonia is "an economy in transition" - in transition to capitalism, instead of in transition to fascism.

Australia and New Zealand, though overall roughly equally socialized to the USA, tend to differ randomly from the US in what is regulated and socialized, and what is socialized tends to be socialized in a different way. Australia has a markedly more private school system, it has private transport infrastructure for resource extraction, and has much more private sewage than the USA.

Various Latin American countries are small enough and poor enough that they go for the revenues from regulatory arbitrage, for example Panama. Lee taking power in Singapore was a revolt against the neocolonialism of the London School of Economics, and thus against Harvard, and thus Singapore does no end of things that horrify the Harvard consensus, such as actually punishing criminals. They nonetheless try not to aggravate the US too much.