She most likely identifies as female and is therefore in the correct changing room. Yes the changing rooms are single sex but if you identify as female and have a penis then you are going to use the female changing room.
No. Single sex is about biology, and actual reality. Sex is not gender. Identifying as a woman, man, panda, alien, whatever, is irrelevant. It's not sex, and the changing rooms are sex segregated.
I work with child safeguarding and 93-95% of child are abused by someone they know. 1 in 9 girls (terrifyingly high) although I suspect higher as many don’t report.
And showing your penis to unconsenting females is abuse. It's flashing. This person could be using a cubicle, one exists, fully self contained with shower. They are choosing to expose themselves to women and girls.
The best way you can keep your child safe is by encouraging them to have strong boundaries, knowing the difference between “stranger danger” and “strange behaviour”.
Exposing your penis to unconsenting females is 'strange behaviour'. The OPs daughter's boundaries are clear - they do not want to be exposed to this person's penis. As a result they are excluded from their appropriate changing room and are forced to used the disabled provision.
If your daughters feel safer and more comfortable going in to the cubicle that is their choice and I would encourage them to continue to make choices THEY are comfortable with. They are both going to make many many decisions throughout their life and adapt their actions and behaviours so they feel safe (which is the reality of girlhood and womenhood).
Women and girls should not be forced to exclude themselves from provision for their sex, it is there for them. Not for male people who wish to be 'validated' by infringing the rights of women and girls.
All of our children are growing up in a world with transpeople and I would continue to have ongoing conversations and trans people in their orbit. Maybe start by correcting the language from tranniemannie to transwomen.
This is the only part of your post I agree with. But they are children, and they are scared and uncomfortable. OP stated they've already had that conversation, which is good.
Also what do you want the outcome to be today when you go to the gym and speak to them? Do you want the transwomen banned from the female changing rooms?
Yes, of course. They're single sex changing rooms. The trans person's sex is male.
Do you want all people with penis’ to change in the male changing rooms?
Of course.
What if this was at school and a trans girl got ready in their school changing rooms? How would you approach this situation?
In exactly the same way. Male and female sexes should be segregated where nudity is necessary for people from the start of puberty, generally the rule is age 8+. Regardless of whether it's a gym changing room or a school changing room. It's necessary for everyone's dignity, safety and comfort.
Including the trans person - one would imagine that a trans woman who wishes to 'pass' would not want people to see their penis and therefore be 'outed'.
I am
not asking you to challenge you I am just genuinely curious as to what you want the outcome to be.
Refusing to let your girls have Snapchat is fair more likely to keep them safe.
Good luck!