At many schools, "safe spaces" are designated by clubs sponsored by the university that meet in university-owned space in a building designated for student activities. That seems appropriate. Classrooms, by contrast, should be professional and constructive places where people agree to argument for the purpose of learning.
I work at a university. I hear from, say, a transgender student that math class is tiring because they have a peer who keeps humming "Lola." I can tell that student to stop taking away from class discussion, but I can't create a "safe space" in my math class by magic. I'm glad my student has a place to go to in the student activities center to figure out a response -- I don't want to be the point person on that! I just want to teach math. Students need other places where they can feel welcome and supported, even if people here on HN feel that it's somehow cowardly and unintellectual to want a place where they're normal, because student drop out otherwise -- the stats are clear.