I think that getting hrt in general should be open to anyone (after a very thorough explanation of what will, won't, and might happen), but it'd not be unreasonable to require a diagnosis for it to not be funded out of pocket.

Though I also feel like the argument falls apart when looked at more broadly, tattoos are accepted by most of society as something adults can do, other body modifications not so much (my first thought is always this guy i read about that allegedly had his nose sawed off because he wanted to look like a fallout ghoul). Modifications like that share more in common with HRT than tattoos do imo, they have permanent consequences that go beyond just looks (not having a nose to filter things should be obvious, and iirc it's not great to go on hrt for a long time and then just... stop, for availability reasons or anything else). Cosmetic surgery in general varies wildly in acceptance and legality worldwide depending on what is done precisely, and some can be dangerous while some isn't.

I am of the opinion that anything you want to do to your own body should be legal, but tattoos are a handpicked example that does not reflect a general social attitude towards body modification.