racist, sexist, authoritarian, superstitiousDon't forget: they might be xenophobic too! Or do we need more xenophobia to protect "democracy and freedom"?
I would welcome Jackie Chan if he sought US citizenship, regardless of any peculiar political comments. Peculiar political beliefs are allowed; it's an explicit feature of the American system.
Any number of "Jackie Chans", when mixed in with all other top-performing immigrants with diverse beliefs, total up to zero chance of making make our society coarser or less free. Highly-productive people who leave their country of birth because they prefer the USA are not, as a general class, small-minded enemies of democracy and freedom.
And even where they have some preferences we natives might find peculiar, within one generation, those peculiarities will either prove their enduring value or be discarded by the children raised here.
As it has been for hundreds of years, so it shall be.
And thanks to American cultural/business exports, telecommunications, the rise of worldwide English, and rising world living standards, each wave of immigrants is already more like us, upon arrival, than previous waves were.