That very succinctly sums up the disconnect on this topic.
People who believe themselves to be something other than the physical objective truth are free to indulge in that. They can play dress up, change their name, get surgery, change their lifestyle, etc, in any manner that they choose. That is where they have rights. No one should be allowed to make them stop. At the same time, anyone who doesn't want to play that game has the absolute right to choose to opt out.
This whole "you can be anything you want" thing is just the modern version of the Emperor's New Clothes. You're being told that you're not allowed to mention what is actually in front of you, but must instead pretend that you see the same thing that everyone else is pretending that they see.