What you're describing is the motte[1] of 'safe space' and 'trigger warning', that is, you are presenting a definition whose application almost no one could object to (of course I don't want to ban minorities or LGBT associating with each other, and choosing not to associate with other people), but the real life usage of the term (the bailey) is different, at least the usage that Bloomberg is referring to.

Yale and U of Missouri recently (last year) served as examples of using 'safe space' to constrain other people's freedom of association. Demanding that the entire university serve as a safe space (even under your definition) is completely different from demanding that there exist a safe space somewhere in the university. The latter may as well be a foregone conclusion, nobody is going to force the student LGBT association off of campus, but the former means the LGBT association has a mandate to censor any student anywhere on campus.

[1] as described here among other places: http://slatestarcodex.com/2014/11/03/all-in-all-another-bric...