Should European nations be doing more to protect their indigenous culture and populations?

Other indigenous peoples have special protections in their homelands, like the Native Americans, Australian Aborigines, Saami in the Lapland, etc. But the EU seems to be welcoming foreigners and their cultures with open arms. European countries aren't America, they have not historically been a melting pot of refugees from all over the world like the Americas and Australia have. Asian countries like Japan and China have stricter immigration laws to preserve their countries so why aren't European countries doing more to discourage non-indigenous immigration?