The problem with all these things we're trying to do is that we have the unintended consequence of really keeping them childish in many ways, and it has become very telling when you look at the level of public discourse today. It starts when they're young and is proving to have detrimental effects that carry on into adulthood as more and more studies come out.
People are becoming unable to maintain a collegial dialogue, like you and I are doing at this very moment (thank you), the notion of ideas that disagree with your own become unfathomable, even traumatic, and then you're unable to see where someone else is coming from. You then can't meet in the middle, because you have to be right and they have to be wrong, and then we're stuck. You can't even, as the kids would say.
I truly believe that to have the hard discussions we need that people need to feel safe to speak their mind. For someone who's lived a persecuted life, they may never be able to do that unless they're in a place they believe is safe. If that means that on campuses different student centers are labeled as such, so be it. That's fine. If the entire campus, all buildings, and all rooms are labeled as such, then where are we going to have a discussion where we disagree? Because taken to the logical extreme that we're seeing, to be a safe place, we can't have a disagreement, it would be too unsettling.
College campuses should be the root of these hard discussions. These are the institutions we're sending our kids to in order to engage in higher thought.
Can we move on from this pretty limited discussion? Most other comments here have made it clear that not every use of "safe space" and "trigger warning" is legitimate, and we all agree with these layups you're taking.