With respect, the words "have to" is doing a lot of heavy lifting there. Surely any onus to integrate should fall more on those arriving than more long-established residents/citizens,
Yes, I acknowledge that the Native Americans (for example) would hold a strong (and probably valid) opinion on this sort of issue, but I still don't think we should "have" to bend over backwards to integrate with other (sometimes very different) cultures. Many will obviously embrace, enjoy and welcome various aspects of these cultures (cuisine perhaps being the best example - though I would personally beg to differ) but "having to integrate"?
Choosing maybe, but there should be no compulsion (as implied by "have to") here.