Not proberts, but observing left wing media in the States over the last 8-10 years I've seen a carpet bombing of the same concept: eliding the difference between immigration and illegal immigration. If you want to talk to your conservative friends and family I'd start by checking whether or not it's illegal immigration they're against. Even the Democrats seem to be noticing that people don't like open border policies and are scrambling to adjust campaign promises in light of this.
I understand you might not able to think in these terms when it comes to the hated enemy, but if you think of all people as people, even Republicans, then you might notice that they don't all think the same things. Or even that they don't hate illegal immigrants, but think that laws are a good idea and criminals should be punished, not rewarded. This is just understanding both sides 101, in case you do break out of this mindset.