Well, in theory anything is possible, but in practice, I’d say I’ve never seen anti-immigrant movements operate at any state or national scale without an undercurrent of fascism. Economically, they reflect a base fear of competition, and socially, they’re predicated on the myth of some sort of singular “American Culture”.
I can see (and I myself sympathize with) being anti-illegal immigration. I also support the idea of regulating trade with nations that have such poor labor standards that they force ethical capitalists* to compete with what are essentially slave laborers. But within the American job market, new immigrants often simply do more for less than those who came before them, without such unfairness or abuses. It ought to be a well-established fact that it’s the perfect antidote to stagnation, but when the fat-and-happy feel the pinch, they’d rather see stagnation than competition. So these fascist movements spring up, same as everywhere and -when such things have happened. What has probably saved the US from recent attrocity is that the natives were essentially wiped out long ago, so there’s no one left in power who can tenably lay claim to the xenophobic nationalism that flourished in Europe, and carry that claim to its most disastrous consequences. I’d say a constant influx of immigrants is a great antidote to fascist movements, simply by diluting them.
*It needn’t be an oxymoron.