If a Ukrainian was to reach US soil, then of course they could legitimately claim they were fleeing war, which is a pretty good basis for asylum.
However, there are international norms and practices, like "first safe country," which means that if a Ukrainian leaves Ukraine and enters another safe country, then they can't jump to another country and have a right to claim refugee status there. Further, this is a European problem, and therefore Europe should take the lion's share of the refugees in any event. That should be especially evident, given that so many folks seem to think the US is racist and bigoted to the core, whereas Europe is enlightened, giving and caring -so, by all means, Europe is a far far safer place than the evil US, which lets people die in the streets, etc.
I don't know about conservatives, but I apply the same standards to similarly situated peoples. One main difference to point out, however, is that a refugee from Ukraine is more evident and obvious than a refugee from Canada or Mexico, since the Ukrainians are literally fleeing war and civilians are being flattened, whereas Canadians are fleeing Justin Trudeau and Mexicans are fleeing poverty. A person fleeing poverty is not a refugee, he's an economic migrant. Not the same thing.