While I appreciate what you're trying to say, and agree that it's draconian. The assertion that they can't force you isn't quite true. The collage is private property, they can absolutely make entry conditional on using this app on your personal device.
If you don't agree with their measures, then you simply aren't allowed on the colleges private property. Just as equally they can make compliance a condition of providing your education (it's a private contract after-all). Again, don't like it, don't get educated.
Ultimately college education is a contract between private individuals, none of the protection you have against government overreach apply.