Is multiculturalism contradictory?

It seems that many who tout multiculturalism (i.e. many cultures living together) also seem to want these cultures to remain separate and not assimilate or mix with each other. Is it asking too much to want multiple cultures to live together but still maintain their own separate "islands" within society? (Cf. the concept of "cultural appropriation", where cultures borrow from each other without maintaining the original culture's framework for what it is they're borrowing. This is seen as a bad thing. But it's inevitable in a multicultural society. I'm seeing contradictory forces at work here).