I wouldn't worry too much about that. The most reactionary people in the US, those who think socialism is communism and horrible labor laws are "freedom," are too heavily indoctrinated into their own little death cult. They honestly believe there is no country more free than the US and are genuinely fearful of the idea of living anywhere else, they would never move to Europe.

People who live in reality, on the other hand, see how horrible it has become in the US and are looking for a real "land of opportunity," where you do not have to be a willing slave to capital in order to have the right to the basic necessities of life. They are fully disillusioned with the "American dream," and so are more open-minded toward socialism, and are more willing to agree that maybe most countries in Europe provide them with real, actual freedom far more that what they have living in the US.

This has been my experience with immigrants from the US, anyways (and, full disclosure, I am an immigrant as well, just not in Europe).