Many schools allow you to apply based on other factors. New enrollments at music schools (not the top ones, but still some very good ones) allow you to take a starter course the summer before school starts so you can learn to read music. Music has changed so much in the 20th century that a prerequisite in music theory isn't going to hinder you if you show the ability to apply your analytical skills.
Having been through music classes myself I noted I was initially wary of those who hadn't been trained musicians since the age of 7, but quickly realised that it really didn't matter and some of my peers really excelled at music having picked it up even as an adult.
Doesn't apply to performance/dance schools though, obviously - you can't get a degree in piano performance if you're just starting at 18, unless you're a rare genius.
