Nobody is against to highly trained, well-educated, rich immigrants (or nobody I’ve spoken to apparently).
Put a proper highly selective, blind, state department administered brutal exam before issuing the visa and you will see how in decade how will the opinion of them will change.
The fact is importing desperate workers burdens community support services, drives up costs for the vulnerable, and undermines living standards by bidding down income levels. =3
Of course people don't like change.
Consider though that we are all descendants of immigrants.
How would you want your descendant immigrants to be treated?
I'd say that depends on whether people are happy with their circumstances.
We can't rely on "what voters say" like the OP suggests, because for some of them what they want to say is forbidden so they say other things instead.
People who are prospering don’t have much negative feelings about immigration or the homeless or drug addicts or any “them” in the “us vs them” dichotomy. People who are not are more anxious and stressed and feel uncertain about their own place. People in such condition have no capacity to welcome others they feel are competing with them on whatever little resources there is to share. It wasn’t long ago that people in cities villainized and hated rural migration into the cities within the same country. As wealth and prosperity increased in the cities those feelings dissipated.
I guess Texans are suddenly in favor of immigration, when 2 years ago they hated immigration.
So when I asked people who voted for right wing candidates how they square the love for their migrant neighbors with their vote, the explaination typically was to point to foreigners somewhere in the bigger cities, but the ones living here are okay. When asked to specify which foreigners and what specific experiences they had made it always turned out that it was just a very vague thing and they haven't made any experience, but read/seen a thing or two in the media. They often couldn't even point to one specific article.
I live in a city now and to this day I will sometimes see (clearly fascist) rural tourists in the subway, that are shocked and scared because they see slightly more people with darker skin tones than they are used to, despite no tangible bad behavior happening.
A lot what motivates anti-immigrant people happens in their heads. And if you're rich that is good. Keep the people divided by skin color, otherwise they may start to think about the other divide.