With the aspirations of "civility and mutual respect" along with "rigorous debate, discussion, and even disagreement", I would hope any truly egregious edge cases disappear.
In the middle, I think people have the right to remove themselves from discussions—civil or otherwise—that they don't want to listen to or engage. But that right doesn't limit others' ability to have those selfsame discussions in public or private venues, nor require others to give you advance warning about it.
And finally, U. Chicago has the right to set degree requirements. If you are unable or unwilling to meet those requirements (e.g., not participating in discussions), then you have no place at that institution. After all, the "real world" won't hold your hand.
So...
Trigger Warnings ("A trigger warning is advance notice about subject material that may be difficult for certain students to read, hear or see.") U. Chicago says they "don't support" them. I think actively discouraging them in every case seems extreme, but the institution simply can't be required to provide trigger warnings in every case for every individual. In other words, a lack of trigger warning doesn't mean you won't be triggered.
Safe Spaces ("A safe space is a place they can go to avoid those subjects or heal after confronting them.") U. Chicago doesn't condone the creation of safe spaces. Similarly, I think this stance is extreme. Safe spaces may be necessary for individuals. But U. Chicago is under no obligation to provide them for you or excuse you from other discussions as a result.
In other words, U. Chicago isn't a place for people who don't want to discuss issues that make them uncomfortable. Which, on its face, seems reasonable to me.