Clearly universities have "personality" (as do all business's) and that factors a lot in which university I choose to attend. I expect a different world-view in say Alabama compared to say California.

I might steer clear of Berkley as being too hippy, and choose Alabama or Mississippi instead.

But I also expect that a business in the business of sharing ideas is open to new ideas. If I want to discuss a gun-free society at Alabama State, then i might be in the minority. As a professor my students won't appreciate it in my physics lecture, but I might form a student group against guns etc.

So yes a university is a business, but the business of ideas, and censoring some ideas seems like that makes it a bad business.