people should be allowed to live where they choose.

I’m not sure if I agree, neither do I strongly disagree. Even though individuals should be allowed to live where they want, communities should also be allowed to decide who they allow to live with them. Collective decisions are the very foundation of a community and what differentiates it from an agglomeration of individuals. Please take into consideration how the latter one would be authoritarian by nature. So, I think both rights are true - that of the individual to freely move and that of the community to build something exclusively for itself - and neccessary for a liberal society. They have to be balanced out carefully.

you almost certainly could live and work in a European nation without being forced to leave in the way these people are

You are right. I am a citizen auf the European Union and hence part of a sovereign community.