I think it's more nuanced than this. The left believes in immigration based on the amount of hardship / suffering endured by the immigrant. The more the suffering, the more deserving they are of being let in.

The right believes in either no immigration or immigration based on an impossibly high bar with caps preventing immigration from undesirable origins.

My view is that in the long run immigration policy simply does not matter because we will have figured out how to educate, recruit, train, and exploit the high quality remote labor from any country. The most talented folks around the world will find a way to reap the rewards of the American economy either by residing within the US or doing it from afar. The after tax wage spread is margin that can be exploited.