Moran writing that anyone who "has a vagina is a woman" (I paraphrase) specifically excludes trans* people. Or to take your example of supposedly "pointless hairsplitting" - substitute "blacks" or "gays" for "transexuals" and see what the reaction would be like.
It excludes by implication about 0.00001% (I guess) of the female population for the sake of keeping her writing sharp & pithy. If you feel you can't be part of a left that refuses to butcher good writing for the sake of bogus self-congratulatory inclusivity, that's fine by me - it sounds like we're better off without you.
As for the "a bit mad"... one instance I particularly have in mind runs roughly like this (I'm paraphrasing from memory - I won't link as I genuinely think the person concerned is a bit unhinged but you can find it via Helen Lewis's posts)
Person A: Why are people praising the racist [person x]?
Lewis: What has she said that's racist? Do you have a link?
A: Oh look who's leaping to the defence of the racist!
Lewis: I'm not, I'm just asking for the evidence.
Person B (friend of A): PoC don't forget racism when they see it. Stop demanding evidence.
and so on and so on
People like that don't need indulging, they need taking aside by a good friend and being told to get a grip.
edit:I'm not defending Burchill's hate piece, which was of an entirely different nature and, tbh, likening hers to Moran's is way more dickish than anything I've written here.