The trouble is that if your lovely friend gets to - and my lovely TW friend and their lovely TW friends and everyone's lovely TW friends -
then so do all TW, plus as you say, any other male person who wishes regardless of whether or not they sincerely have transitioned, plus the Whites, Yanivs, Chapmans and Kardashians of this world. No one is going to stand on the door and check whether each one passes (and what a cruel thing to do that would be) or stand up to those like the burger throwing individual who will shout and rant if challenged because they present entirely as male and want the right to go where they choose when they choose.
The common denominator here is total disregard for the fact that this is a female space, meeting the needs of female people, and its first duty is to provide inclusion and facilities for those female people.
And once any male people are using it, it's a mixed sex space, and we've excluded some females from any access from any facility to give male people their preferred choice and best wellbeing out of all the available facilities. Which is obviously appallingly - well not sexist, it's flat out male supremacist. It sees the needs and wishes of male more important than considering the basic rights of access and equality of females.
What are we going to do with the females who can't use mixed sex spaces? What are we going to do with no female spaces at all? Where every space is one that any male walks into at any time?
We tried a compromise. Some few TW, sincere transitioners, that was the plan. It was called the GRA. It's failed. Look at it failing for females. Male people have proven that they cannot respect female people's needs or boundaries or even allow them basic consideration, and that any access for any will mean forced total access for all, regardless of impact on females.
This is male people's problem to solve now, in finding how to be more inclusive and support the needs of all males. I understand this is sad and upsetting for the TW who have been used to access, but they need to take up their sense of loss with the people that pushed female good will until it broke.