DanGleballs
We don't have to agree on everything 
.
I'm leaning slightly to one side and you are leaning slightly to the other. We agree on most of it.
My position is that 'making a significant effort' doesn't mitigate the reasons or the motivation in the slightest. Lots of men with autogynephilia do make a significant effort. Their goal is to 'become a woman', to wear a woman's skin.
The bottom line is, there is absolutely no way of knowing if the man in your space is getting a kick out of it, is a predator, is a brilliantly passing transmen, just wants to pee, is a rapist, or has walked in by mistake.
And you either consider that women have the right to deny them entrance, or consider that the few trans people with authentic gender dysphoria should have the right to enter to make them feel comfortable, despite objection, and open the floodgates to everyone.
Sometimes you just have to pick a side. It doesn't mean you don't have compassion for people or you would rather be inclusive if you could, or any normal human traits.
But sometimes you get forced into a position where you have to make a choice.
Personally I would like to see a third category called transgender. Their own rights, and spaces, their own sports and their own specific needs. But they don't want that. They want women's.