I think this is a really tricky one. Trying to be even-handed, fair and reasonable here:
I've read the 2nd article from the Washington Post, (not a sensationalising newspaper - more like the Telegraph I think) so commenting on that. The article doesn't say whether or not the transwoman involved, Lila Perry, has undergone counselling or detailed discussion of her choices & feelings. It simply says she hasn't had gender reassignment surgery, but decided at age 13 that she was a girl, and dresses & lives that way. So it's not clear there's even been hormone treatment, which I assume would "shrink" the size of ale genitalia and render them pretty useless? I don't know, so could be wrong there.
I can't help wondering if this is a homosexual boy, or a non-gender conforming boy, caught in a very conservative community, and so the only way s/he can square that circle (to his/her mind) is to "become" a girl so her sexual attraction is opposite-sex not same-sex. That's just speculation though ...
There doesn't seem to be any suggestion that the girls are at any risk from this person's presence in the locker room. But we don't now whether anything she said or did really overtly made the girls uncomfortable, or whether the transwoman (if she is that actually!) was combative or confrontational.
BUT ... at the ages of 13-16 or so, a lot of girls are compliant to our culture's socialisation about modesty in front of the opposite sex during puberty, and may feel that Lila Perry's presence is a challenge to this and an invasion of their privacy. I don't like this socialisation around modesty & keeping girsls and boys separated. BUt on the other hand, it's in teenage years that boys learn and are socialised into masculinist roles which include violence, harassment & aggression against teenage girls. So there are good reasons for segregation.
So this is where it's difficult: I don't really want to align myself with the Christian (sounds fundamentalist) father who is leading the legal protest. Who says stuff about wanting to control what his daughter knows/sees about the opposite sex.
And I can feel for any teenager being forced to do things differently ie use a "special" changing room. I can also see why the boy's locker room & showers would be quite perilous for a teenager undergoing transition - IF hormones have been involved (no mention of the medical and counselling aspects of transition).
To be fair to all involved, it's a tough one ...