No, not really. The GOP overall xenophobia and racism is well do ented, there's nothing imaginary about it. The South, a bastion of conservatism, is particularly adept to white supremacy. This is quantifiable.
Fact is this country was put together by immigrants and that has always included illegals as well. Heck, the last big amnesty we had was done by none other than Reagan, a stalwart of the GOP. But he was smart, that locked up the Cuban vote in Florida, for example.
There are actually completely valid reasons to secure the border. You could point to heightened security for example. But in that case you don't need to denigrate immigrants calling them rapists or criminals. Unfortunately, the GOP base is not really sophisticated, and the brown skin boogeyman still works well there, tbh.