The thing is, Romanians are Europeans. They're all culturally European. It's just that some (mostly Western) Europeans dislike the grimier aspects of European culture and have redefined European-ness to exclude some European people.
If I see a hobo from Alabama begging downtown, I'm not going to be like "this guy is not 'culturally American,' we should restrict Alabama's travel to the rest of the US." I see it as American culture, and we should fix it by improving quality of life throughout the federation.
The "unified Europe" project is hilariously wrapped up in mindfuck games of who to exclude.