The USA prosecutes people who go overseas to sexually exploit children. Even if it’s not illegal (or enforced if it is) where they did that. It’s not unthinkable that politicians in some red state could enact legislation that made travel or abetting travel for the express purpose of obtaining an abortion illegal. I doubt they could prosecute the doctor/clinic personnel in the blue state, but they could go after the woman and anyone who knowingly assisted in the travel (paying for plane/bus/train/Uber fare, loaning a vehicle, actually driving the woman there, etc). Just maybe not for the abortion per se.
The problem, logistically at least, is that, unless someone decides to make themselves a test case like Larry Flynt and his buddies with challenging anti-pornography laws in the 70’s, you can’t really know why any given woman is traveling from Wyoming to Minnesota. We don’t require women to register their menstrual cycles, thankfully, so it’s impossible to know if a woman is pregnant (she could just be fat). So, without a massive surveillance state, it would only be applied to women and their abettors when someone decides to tattle on their pregnancy. Or as a matter of revenge when a relationship goes sour.