Depends on your definition of "immigrants".

Sure, you might think of it as "people with citizenship of another nation."

But I suspect it's more along the lines of "people who don't look like me."

White Afrikaaners are welcome (we'll even invent persecution and call them refugees), but folk from elsewhere (ie actual refugees), um, less welcome.

The trope about "culture assimilation" also comes up. It's OK for Irish and Italian immigrants to keep their culture, adding to the melting pot, but Mexicans and Africans less so

And sure, lots of people are friendly to "the immigrant they know" while at the same time being very against "immigration". One need look no further than the last few elections to see this in action.