I'm not informed enough on how legislation works.
But personally I would remove gender re-assignment from the equality act. I absolutely believe it was inserted for exactly this reason (AGP normalisation).
I disagree, profoundly, with the entire concept of transgender ideology. I understand that the idea put across was to allow some men to cross dress, in order to salve their inner turmoil over being men, of course. But it's sexist. And should never have been written into legislation (and the equality act of all places).
In specific terms of HR at Hayton's school. They could write a school policy of no fetish gear at work. That would stop him in his tracks. Because he's told them that's what he's wearing.
And again, if there's pushback, let's bloody have it. The only way we get all of this nailed down, is to get it out in the open, examine the laws and what they mean, see if they're correct, fair, and based on evidence.
And I don't have much of an opinion about whether to reinstate the word transvestite. A lot of people understand it, yes, but it's my understanding that the two conditions aren't identical. AGP is an escalation of transvestitism.
But maybe in terms of recognition, it's a good idea to use it.