Hi, fellow North Carolinian (presumably)! I saw that you’re looking for a larger co-ed school-- have you checked out App State and UNC-Wilmington? They’re two of the more rigorous public schools in the state behind UNC-CH and NC State. I get the sense that both have a very healthy range of political opinions-- both my friend (raised by parents similar to yours) and myself (very liberal/agnostic) really like App State.
Edit: I just realized UNCW may not have a dance major. App State apparently does, though.
Edit 2: From looking at dance programs here in NC, UNC-Charlotte and ECU also offer dance programs. UNCC might be a good one to add to your list-- the business opportunities in Charlotte are great due to it being a finance center, and it’s a large enough school that political beliefs really vary!