I don't think the issue is so much about discrimination as it is about practicality. The reality is that we live in a society where people don't like sharing restrooms with folks of the opposite *** (yes, ***, not gender. just to be clear). As long as that is the case, broad adoption of unisex facilities isn't going to work. Which leaves us with the much more expensive per person individual bathroom model or just accepting that the very small percentage of people for whom this is an issue will have to deal with it. Ultimately, it's about making one of two groups uncomfortable. One group represents a much larger percentage of the population. Again, it's about practicality.
The issue with the 6 year old kid goes far beyond the level being portrayed right now. The question is how far the rest of society has to adjust to make room for one persons self-image? It's all well and good to say that we're infringing his/her right to be a unique snowflake or something, but the problems don't stop at the grade school level. What happens when it's the locker room, or the showers, or sports? Expecting the whole rest of the world to make way for your own personal preferences is a bit silly. We have social norms for a reason, and fair or not, it's a **** of a lot easier to find ways to adjust to them, rather than make everyone adjust the other direction. This kid is going to encounter problems with his desire to be female for his entire life. Better he learn that now and figure out ways to deal with it, than run headfirst into block after block after block.
I may feel that wearing a black tie outfit to a black tie event imposes on my own personal sense of style, but guess what? I'll wear the **** monkey suit anyway. Why? Because it's a lot easier to just conform to the expected norm than to do my own thing. I kinda see this the same way. Get used to having to comply with social expectations because the world is full of them, and there's no end to the kinds of non-conforming actions one might demand they get to do instead. No one's saying you can't wear a dress if you want, but perhaps it would be better to teach the kid now that he will face problems doing so than fill his head with the false belief that the world will bend to his own desires and let him do whatever he wants.
Is that unfair? Absolutely. But in the long run, this kid will be vastly better off having realistic expectation of the world around him.