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I went to a couple religious schools there because I was chasing a degree and they were my only options. Don't even consider any of them, they're honestly cults that don't care about education or student quality of life in the slightest. Honestly if you're a highschool senior that's looking for somewhere to go, just go to a community college for 2 years to get your gen Ed out of the way and pick a 4 year later. It saves a shit ton of money and community colleges are based as fuck when it comes to the staff. Since there are usually not any dorms the professors usually give a shit about their students' time since they're not forced to be there.
To answer your question though, you're kinda fucked. You can't expect to go to a state university in any state without it being liberal. If you're talking about student body, outside of UNC Asheville or Chapel Hill, since NC is in the South, there's much larger political diversity than a lot of other states. This means you can go pretty much wherever you want desu.
As a side note, trying to find a right wing echochamber to live in for 4 years is just as bad as the left doing the same thing. Just cut that shit out.