Who gets to define "women-only" spaces?

I'd love to link to the original post without referencing the ensuing shitstorm that followed, but I think it's important as a teaching tool, and as an example of some of the virulent transphobia that is still all too prevalent in feminism. Twisty, from I Blame the Patriarchy decided to make her site open to women only. Of course this includes trans women -- because they are women. Unfortunately judging by some of the comments, not everyone thinks so.

Feministe also weighed in:

I do think there’s something to be said for creating women-only spaces, under certain circumstances and for certain purposes. Twisty at I Blame the Patriarchy has decided to make her blog all-woman all the time, and received some immediate push-back in the vein of “But what about trans women?” To which I would reply, “Did you see the part where we said this is a women-only space? By definition that includes trans women.” And yet there still seems to be some debate about this? -- Jill from Feminsite

Knowing feminism’s history (past and recent history) of transphobia, I’m not sure how I feel about this. Echoing some of the Feministe commenters (I can’t load IBTP), what about non-binary people? I’m cis, and the fact that mostly cis allies seem to be doing most of the deciding who can and can’t participate depending on their gender bothers me.

The idea of women-only spaces in general? Eh, it's her blog; she can moderate it whatever way she sees fit. I can surely understand the need for places where women can discuss things without men's "input" (the unchecked privilege, the need for mansplaining...), but it also implies all women's experiences are equal, which absolutely isn't true. (Something Twisty did touch on but got a little lost in the comments.)