If, for say, I want to apply to a school as an Acting major, and go through and audition but do not do well, will the college still let me into the school under a different major? I want to apply to Ithaca College in a couple of months and I primarily want to go into their Acting program, but I want to know what will happen if they decide that my audition was not good enough. My GPA is pretty high and my SAT/ACT scores are good. Should I instead apply as undeclared and then later on change my major to Acting and audition then? Which way will give me a better chance of getting into the college?
If you are not accepted into a BFA program, but are academically qualified, some schools (including Ithaca) will offer the chance to choose a different major. For others (NYU, and Boston are examples) it is all or nothing. You have to check with each school on your list. At Ithaca, there is a theater studies major that requires an interview (rather than audition, and it can be done over the phone) I know a couple people who loved Ithaca, but weren’t accepted to the BFA program, and went that route instead.
Just echoing what @toowonderful said. My son applied to three majors at Syracuse (acting, MT and communications) but was not considered for anything but acting after he auditioned. (He would have been in the top 5% of their class academically, so it wasn’t a grade problem.) We were told that you could apply to two majors at CMU (say, acting and English) but that is unusual.
Pace is notorious for pursuing rejected BFA candidates for other majors, sometimes with very good aid offers.
I would call what Pace does more “hounding” than “pursuing” 
I had it as “hounding” on the first write, but it seemed judgmental.
It’s a fantastic artistic program if you are admitted, so no “judgement” there- but I have not ever heard people praise their admissions department… On the other hand, the only time you are going to deal with admissions is before you go- so I wouldn’t recommend choosing/not choosing a college based on that
I think U of Minnesota will let you pick another major – they accept you academically first and then they send you to the BFA program for the audition.