Huh? Most universities in the US are private, including the large majority of the top ones that host controversial debates. (All the Ivys, Stanford, MIT, CalTech, etc.) These universities are held to rather high standard of neutrality even though it's not legally required for them to do so (modulo restrictions from government grants, which are empirically not the main drivers of their behavior with regard to free speech). They behave this way because the university professor and administrators believe the world is better for it, and because otherwise the public would lower their esteem as honorable places of learning (and good places for donations!).
> Free speech is narrowly intended to be something that limits the government's ability to impose restrictions on non-government entities for good reason
No! The First Amendment is intended to limit the government. Free speech is a much wider concept! If you don't understand why free speech is an idea that has important moral implications for individuals and private organizations, you should read "On Liberty" by John Stuart Mills, the classic canonical defense of this. It's only 100 pages and available free.
https://socialsciences.mcmaster.ca/econ/ugcm/3ll3/mill/liber...
Honestly, I want Liberty to support open and honest debate. Otherwise, what is the point of having a university? I understand that their professors are going to be required to sign their statement of faith. Such is not required of the student and students of all faiths are welcome.
Public universities. I wouldn't dream of asking the same thing of Liberty University. The difference being, the one is a branch of government, and the other is not.
Free speech is narrowly intended to be something that limits the government's ability to impose restrictions on non-government entities for good reason. Asking private organizations (e.g., Liberty University) to follow the same limitations would undercut free speech by preventing ones with a particular point of view (e.g., a conservative Christian one) from actually being able to express that point of view.
Now, if we all wanted to agree that Facebook needs to be granted common carrier status for publicly arguing with your family about politics, that would be different.