I read about this and I am having a hard time finding an article that isn't sensationalist, so I'll just put here the post I made elsewhere about this (even though it will probably be buried due to the number of comments already posted).
Currently, there are separate men and women's locker rooms, restrooms, etc. Women have historically been prone to harassment/assault/etc., trans or not, so I'm not a fan of making locker rooms unisex for safety reasons at this time. With that said, I think this situation is tough. Let's say you are female in a locker room and a person that looks like a man comes in. Most women would get very anxious about this. Especially if they are survivors of assault. The person who came in may say they are trans, but especially if they only just started trying to transition this may be "hard to tell". So you are left trying to decide if the person is being truthful or if they are lying and potentially a danger to you.
For the stickier part: I believe the woman lost her membership for talking to other members about the situation. Let's say in the above scenario you didn't believe the person was really trans and you thought PF wasn't creating a safe environment for you. You would probably warn other women in that case that there is a perv pretending to be trans so he can get into the women's locker room. OR, on the flip side, you believe the person is trans and you want to let other members know not to be freaked out that there's a person who looks very much like a man that will be using the women's locker room so they don't think that there is a perv. Some may argue the latter is not "your place", but I think most women would feel a little responsible for helping other women by either (in scenario one) letting them know there was a creeper or (in scenario two) letting them know someone *wasn't* a creeper.
There's really no 100% win here. On the one hand, it's awesome that PF has a strong policy supporting a harassment free environment. Implementing this is not always non-trivial. In this particular situation especially it appears hard because it sounds like it was difficult to "tell" whether this person was really trans or not. Which means that although the woman is now under fire for being transphobic, if the facts had played out differently and it turns out the "trans" person was really not trans but a creeper, she'd be praised for speaking out against PF and PF would be under fire for not protecting its female members. As it stands, since it turns out that the trans person really was trans, it seems like people are feeling pretty favorable toward PF. On the same token it seems like in an effort to create a "safe space" for one group they created an "unsafe space" for another.
Please note that I am intentionally trying to keep my assessment of the situation as though the woman who made the complaint is NOT transphobic as I can't tell from all the sensationalism whether this is the case or not so I'm just trying to assume the best case scenario.