"I happen to see trans-women as just women. I don't go around demanding people prove gender by showing me the contents of their underwear. There are probably several transwomen in this group and all the CIS ones have no idea."
You haven't even considered why this Facebook group wishes to be female-only, have you?
"What's important is not excluding others without valid reason."
Well, let's consider their reason, shall we? Over the past few years I have heard of many Facebook groups which have been set up for a particular interest and which were mainly of interest to women. Knitting, crochet or somesuch. They were not set up as women-only groups, it's just turned out that they became so. Anyone could ask to join, men just didn't.
Then, someone new asks to join. Maybe they ask if it's OK that they're a transwoman because it seems to be an all female-group, maybe they don't. Regardless, they are welcomed into the group, because transwomen can be interested in knitting / crochet / whatever, right?
Only it soon becomes apparent that discussing knitting and sharing patterns is not on the new member's mind. Instead of posting a picture of a recently-completed project, they start posting pictures of themselves in a variety of outfits, asking for the group's opinion of the outfit, fishing for compliments. The outfits may be unremarkable and raise no red flags per se. But that's not what the group is for. No other members do this, just this male. He has not joined to discuss knitting. He has joined in order to acquire a captive audience for his paraphilia.
Now, some members will "be kind" and will say ooh that's lovely, don't you look nice. Some will say nothing and think can we get back to knitting? Emboldened by this response, the male will abandon all pretence at interest in the group's raison d'être and will begin to treat it as his Source of Validation. Constant fucking me-me-me posts, getting snitty if he doesn't get the response he wants. Members silently leave the group because this wasn't what they were here for. Some may give their reason for leaving quietly to the group administrator, who may despair because they're watching the group be destroyed by this one person, or the may be the BeKind kind who says 'and don't come back'. Whatever, membership dwindles, engagement dwindles, the male get louder seeking Validation, compliments, women treating him as (he thinks) a woman.
Ex-members miss the group, this was something thy enjoyed, dammit! One or more of them bites the bullet and takes on the admin of setting up a new group and contacting other ex-members to see if they're interested. The group either goes private, or states openly they are female-only. (Being openly female-only makes the a target for Seekers of Womanly Validation, but the admin remember how their beloved ex-Group was destroyed and hold firm.)
Of course, you probably don't think that's a valid reason. But those running the new groups do, and so do I.