I've noticed that if people are asked simply if they'd mind 'gender-neutral' toilets - which have existed in various places for some years - they're generally fine about it. Why would they not be? There doesn't seem to be much of a threat, does there?
If the questions were posed - and I can't see that they have been so far - such that the following were asked:
Are you happy that a woman who asked for a woman to peform her smear test might find it's a TIM, complete with penis and beard and she'd be accued of transphobia if she refused?
*Are you happy that TIMs (or men claiming to be TIMs for the purpose of entering such a space), complete with penis, would be able to be naked in a gym or pool women's changing room alongside you, your 13 year old daughter and/or your 3 year old granddaughter?
Are you happy that TIMs (or men claiming to be TIMs for the purpose of entering such a space) might be able to take places in a women's refuge or apply for jobs there?
Are you happy that TIMs will be able to enter women's elite sports and thereby ensure that no woman can compete at elite level and hope to win again?
Are you happy that TIMs (or men claiming to be so) will be able to take scholarships, jobs, places reserved for women previously to try to improve conditons for women?
I doubt there'd be much "happiness" expressed at all.