All of this is true, it does not change the fact that a University cannot regulate consensual sexual activity. The Supreme Court held that a state does not have ANY legitimate interest in regulating consensual sexual activity. The rule would not pass any level of scrutiny. It's pretty cut and dry. It really isn't even an EoAA issue, the state simply can't do it.
It's really not a matter of positive liberty vs. negative liberty. You are talking about a potential state action. You are literally talking about a scenario the Constitution is protecting the individual FROM state action (negative liberty). I don't think you or I have talked about this scenario under the concept of a positive liberty.
As far as limiting speech and association, yes. The state can always limit freedoms, but they need to have a legitimate state interest. For example, the state has an interest in stopping people from yelling fire in a crowded theater. Once you find the state interest, you can get into the scrutiny and the level of scrutiny needed to justify a state action which limits Constitutional rights. I am well aware that you can limit freedoms. Some people might argue the state has an interest but as of now (and it would be shocking if it ever changes), the Supreme Court has held that the state does not have any legitimate interest in regulating sexual consensual sexual conduct.
I'm not trying to be a jerk. But this is a pretty cut and dry case. It isn't even really debated in the legal community. Until this happened, I had never heard anyone try to make a legal argument that the state can regulate consensual sexual activity. I've heard arguments they should be able to (there are people who think Lawrence v. Texas should be overturned).