I don't think being pro-amnesty or pro-open borders or whatever you'd like to call it is conservative.
Absolutely. It's just foolish pandering to special interests of some ilk.
Open borders is allowing one individual of their own free will to work for another individual of their own free willing to hire that person. I would think that maximizing individual liberty was conservative.
I will add that in today's world, this is not a practical situation.
Each state in the US has "open borders" with the other states. And this has been good for everyone. The EU is trying to duplicate this with the United States of Europe. I think we could have open borders with Japan, Sweeden, Ireland, Australia, Singapore and a few other countries. And this would be a good thing.
Border control and tariffs are imperfect responses to an imperfect world, but it is the best we can do.