Protections and the law
All universities, colleges, and other places of higher education that get federal funding are covered by Section 504 which states that they cannot refuse admission to a qualified student on the sole basis that they have a disability or chronic medical condition (like CF). Most notable universities and colleges have a department that works with students who have disabilities. Generally referred to as an Office for Students with Disabilities, this department general helps students with disabilities or medical conditions get the accommodations that they need to succeed at college while maintaining their health.
Any time a college, university, or other place of higher education has no specific department that deals with disabilities, their administration department will usually be the source that works with students and their parents.