Another fear of open borders immigration, especially by those on the Right, is that the immigrants (assuming they become citizens) will vote for someone other than their political party.
Aside from the fact that suggesting someone should be denied the right to improve their life because they might think differently from you is a pretty terrible reason, there is a larger issue here:
Isolating, demonizing, and criminalizing immigrants is certainly not the way to endear them to your cause. Ironically, the actions taken, primarily by those on the Right, will drive them right into the arms of their political opponents. In other words, this fear was created entirely by the Right and is driven entirely by the Right. Not smart.