Assimilation is subjective.
Not really. It's still happening, but it takes time. I work with a lot of hispanics, mostly second and third generation immigrants. Most of them don't speak spanish at all, but they still eat plenty of Mexican food. It's part of their historic culture and no one expects them to give it up. Yet they live as Americans, work as Americans and many of they have fought for America. They are totally assimilated.
"Assimilation is a process in which persons of diverse ethnic and racial backgrounds come to interact, free of these constraints, in the life of the larger community."
Not subjective at all.