I am a man (stating this for the purposes of transparency) and 'identify' as one (to use the language that TAs would use). I have contributed to a few of the threads exhibiting concern about the proposals, in particular that on Hampstead Ladies Pond.
Whilst it may only be 5 or 10% of MN users that have contributed to threads on the issue, I think these represent a significant minority of MN members.
It seems to me that very few if any of those raising concerns about self-identification have any objection to someone who have completed gender reassignment being able to participate in any women-only activity, except perhaps competitive women's sport. Even the objection to self-identification is largely in defined circumstances, such as where women are changing, in swimwear, and sport.
I applaud Justine Roberts for her stance on this.