What I think this thread illustrates above all is a clear and compelling need for third spaces, in addition to single sex spaces, as standard.
I get that this would be costly, and I also get that this is the UK and space is not at a premium. The problem with solely mixed sex facilities is that instances of sexual assault have noticeably increased since 'changing villages' became more common. These statistics are easily Googleable.
The problem is - surprise surprise - men. Women are not the ones doing the assaulting in changing rooms. And assault is depressingly common. Which is why I believe that as parents we do have a duty to teach our sons proper boundaries.
Of course OP's son is precious. So is mine, to me. So are other people's daughters.
As mother to a son, the onus has been on me to work around this and to model the right response to my male child. I've taken him to swimming lessons at my gym from 3 months. The gym has only single sex changing facilities. Sending him alone into make changing facilities is a non-starter. So the solutions are: dad now takes him to his swimming lessons. And I've taken DS off my gym membership. If I want to take him swimming, I take him to a nearby public pool with mixed sex changing.
I would of course prefer to take him to my own private gym. But this is no longer an option. I've put this in writing to the gym, and spoken to them about it previously. They have 'no plans' to introduce mixed sex changing, and in any event I wouldn't want that to usurp the existing single sex facilities.
It's inconvenient, for sure. But when we live in a society which has prolific problems with women's boundaries being eroded by men, It hardly helps if we bring up our sons to have similar values.
It's particularly galling, given the effort I've made to maintain this stance, that my gym made the national media for allowing a trans 'woman' (with a large erection) to use the female changing area. Situations like this are why women's positions are hardening. Clearly, something's got to give. It should not automatically be assumed that that something will always be women. Frankly, we are tired of it.