Hi OP,
Feel a bit sorry for you re the ‘cis word’! You won’t make that mistake again! Moving on...
I’m pretty new to this issue too, I hadn’t really been aware of the debate, shamefully and I have spent the last few days reading a lot. I agree with the majority of posters here and stand alongside JKR / alongside women for all of the reasons variously outlined.
However I know that’s not what you were asking and I have seen a few posts from women who support TWAW and the Harry Potter traitors.
The main agreement seems to be that we aren’t being kind enough 
So, I’ve seen comments such as:
‘Can you imagine being a transwoman in a male prison or male changing rooms? How vulnerable that must make you feel? If you are living as a woman - live as a woman’
‘Women should be inclusive. Trans women are at risk in places such as male prisons, why can’t we share our places? I don’t feel threatened’
‘but there is more to being a woman than sex. Why can’t we recognise that and allow trans women to live as they would like? What are the actual risks at any scale? Surely we should be supporting this minority’
Etc etc. They are all pretty simplistic statements that lack and critical thinking. That said, I haven’t seen many comments from women supporting the ‘cis’ statement or people who menstruate terms. Probably because they’re ridiculous.
What I keep waiting for is someone really high profile to come and support JKR. I just feel there is a pile on and those in public eye should be AT LEAST defending her from abuse, ideally standing with her. But although she has an army of supporters, no one famous seems to be putting their head above the parapet. It’s so disappointing.