Opposition to immigration in the U.S. is usually racist, so members of racial minorities see it as an attack on them.
Not to put too fine a point on it, but have you considered that the vast majority of Americans are descended from immigrants, unlike in Britain and in other countries? That makes us more likely to empathize with immigrants because of our family histories—we also have a national story of being a refuge for immigrants which is contested by many white Americans, but still powerful.
Finally, opposing immigration forces governments into cruel and nasty behavior toward poor and vulnerable people, and if you find that immoral, it drives your decisions.
So, no, it’s not a brainless, mindless “Pavlovian” response by drooling dogs barking “HATE TRUMP”, but a long-standing belief system informed by the history of the U.S., morality, ethics, and a sense of nefarious beliefs behind the opposition.
Considering how much of a positive impact immigration has had on America economically I also don't really understand why the right is so opposed to it. Well it's because the right in America is more an angry illogical movement, and you don't have much of a sensible liberal centre-right.
The foreign born population of Britain is around 15% and I'd be willing to bet a majority is 'descended' from immigrants.
Now many would contend that lots of immigration is 'nasty' towards unskilled native workers; and I think that a lot of the backlash is not born of xenophobia, although that helps, but because of a fear of job loss and the like. It's fairly clear to me that in the long run immigration is a positive for non-immigrants but one does not have to be racist to disagree. Calling opposition to immigration racist etc. has done a good deal of harm to liberal movements I think.
Why do you have such a contigent - likely noisier than big - who are against the very idea of borders? I do suspect that Trump has accelerated support for immigration amongst Democrats simply because one often defines oneself in opposition to something rather than in support of something.