Most are, not like Mexico is our enemy and sneaking over to commit terrorist acts, but not anarchy (not completely undocumented) with no checks. Most libertarians think people should be able to go back and forth to work, or contribute to the economy as tourist, with the only restriction being on criminals.
99.999% of conservatives would trade "open borders" (whatever that means), abortion-on-demand and gay 'rights' (govt out of the marriage business) in a heartneat for a complete rollback and repeal of the left's radical anti-liberty, anti-Constitution agenda.
Conservatives are not statists. Conservatives want what libertarians want - Big Govt to fuck off.
The problem with libertarianism on the culture front is the vacuum is it leaves. If you sit back and allow the left to shape and control the culture, you end up with a socially decrepit, dysfunctional society which will always lead to more statism. It's just not feasible to shrug and "live let live" with radical degenerates like aaaktard, Pelosi, Obama, etc. always in the picture.
Never forget politics is downstream from culture (RIP Andrew Breitbart) and that small govt is only feasible when citizens are morally responsible and independent (conservative values).
I do agree that the GOP has become just as statist as Democrats, but that's what happens when you centralize all so much power over the last century - party politics
is corruption.