How could they not be? If people cannot emigrate to the US then they won’t settle there. A relatively open immigration policy absolutely helped make America diverse. I’m pretty sure that’s what OP is referring to, not DEI or whatever the latest boogeyman is.

I don't think open immigration in America's earlier years stemmed from a desire for diversity. It was more like "holy shit we need workers, I guess we can tolerate some Irish and Chinese people if we have to". It seems like a reach to call that a "diversity policy".

Nor did I claim it was. A diversity policy is a policy that increases diversity, whether it is the specific goal or not.