And if I come back wearing prosthetic ears, is that a felony?

No, it isn't, and it isn't how property law works, either. Free and equal access to private property has been bandied about for decades, and leans away from your interpretation.

There is no such thing unless the property is something like a restaurant or hotel and you discriminate based on a protected characteristic (race, mostly).

PS: The law is all about edge cases if you don't know the specifics you really have no idea what's legal most of the time.

Vis-a-vis beach access: the exception arises in that context because the waters of a state and all submerged land and land up to the mean high tide line are public property. Thus, while you remain free to revoke license to use your property arbitrarily, you can't use that to unfairly monopolize access to public property.

The fact that it's an educational institution doesn't make its property any less private. IIRC, the fact that MIT is engaged in interstate commerce with the public brings it within the domain of the Civil Rights Act of 1964 and the Americans with Disabilities Act of 1990, but those laws carry only very specific limitations: MIT can't refuse someone access solely based on their: race, color, religion, or national origin, and must make reasonable accommodations for people with disabilities. Those regulations on the use of MIT's private property don't make the property any less private than any other such regulations, nor do they in any way prejudice MIT's rights to control access to their property for any other reason.