I’m currently a junior in high school. If I were to take, for example Calculus 2, at a community college, would I be able to skip this UC approved course if I attend a private university? Without taking the Calc BC exam?
You would need to check with each college/university on your application list. Some will accept the CC credit. Some will accept an AP exam score. Some will accept both. Some won’t accept either. There is no way to know without asking each of them individually.
If you also take the AP test, you could be double covered in case a college accepts one but not the other (but you won’t get double credit).