The moral obligation to allow equal participation of different groups who are already here follows from the concept of democracy. But that does not imply anything about how people within a country should view prospective immigrants. That the founders embraced certain principles because they were dealing with a union that already included disparate groups. They never confronted, much less addressed, the prospect of immigration changing the culture of already established communities.

The moral question here is more fundamental than your over-generalization of the founders’ intent. Human beings have a right to self determination, and they have the freedom of association. You don’t lose that right just because you were born in America.