DecomposingComposers Even though the risk to men is not the same, men and boys have the same right to privacy and dignity as we do. If you are female and wish to externalise the sex stereotypes associated with the male sex all the way up to and inxluding artificially augmenting your female body via cross sex hormones or have radical cosmetic surgeries to construct a simulacrum of a male body, that still doesn't make them men.
However females with such severe gender dysphoria that they go down the medical route typically do not wish to expose their bodies to anybody, neither males nor females. If they pass - and many more medically transitioned females pass than males because testosterone is a hell of a drug - they may still not seek to strip naked in front of males because far fewer females who identify as trans have phalloplasty than the other way around.
That's because this operation typically has a lower chance of success and carries greater risk. Females have died as a consequence of this operation, others struggle to live with the botched results.
The prevalence of such females is also much smaller than that of males, about 1 in 34,000 females have such severe gender dysphoria that they go down the medical route and a tiny percentage of them chose to have phalloplasty. (This is for adults. With ROGD and the affirmation model the numbers for juveniles are still unclear).
Female crossdressers for sexual gratification are also extremely rare, heterosexual or bisexual AAPs even rarer. So there are - by some magnitude - far fewer females who may convincingly present as male enough that their presence in a female-only changing room may alarm the other women and girls and even fewer who would get off on using the men's. (Although judging from what females who identify as trans actually say about their attitude towards their bodies, most would use a third space if provided.) And it's not like this is a novel problem - masculine looking or presenting women are frequently in this situation and know how to diffuse it.
So to answer your question, such females, if they don't wish to use a female-only facility so as not to alarm the females using it, will self-exclude from female-only spaces. They do not necessarily then use the men's, at least not until they pass undetected (which in the case of open plan changing rooms is highly unlikely) and look for alternate arrangements.