I think there are mix of issues going on here that are getting handled oddly.
1) Debating ideas versus the validity of groups. In my opinion if there's overt racism, there is room for the campus to intervene to make sure they have an inclusive environment. However if they're debating something (intentionally picking something else) like whether or not there should be dogs on campus or whether or not dog owning is a good idea in the abstract, this is a completely fair discussion. Unfortunately both types of discussions are happening which is making the debate more difficult.
2) Offensive speech Some people will hold and express ideas that others find offensive. As long as this speech is not designed to directly dehumanize or devalue contributing members of the community this probably has to be allowed to have a healthy dialogue.
3) Lots of poor judgement. I suspect many of the incidents (other than the overt racism which is separate) that have crossed the line were not intended to be offensive, but I think some of them were deeply offensive. If you do something deeply offensive I think it's reasonable to be received with a somewhat hostile reaction (demands for apology, anger towards group, etc). This is probably not the most effective way to engage people, better to try to explain why what they did is deeply offensive. I think it's completely reasonable for the school to try to encourage a positive, thoughtful interaction between people without trying to police every minor injustice.