As you say Positrans it comes down to freedom of belief, and the right to be agnostic or atheist regarding that belief and to hold beliefs of your own.
All fine, so long as neither attempts to force their belief system on others, to compel it by law or to create imagined crimes of heresy.
In this sense: there has to be respect for and space given to female people who believe in binary biological sex, and perceive people by their sex, and require privacy, dignity and ability to group by sex. If that was not under attack, I doubt anyone here would be bothering to debate. It is perfectly possible to respect TW belief by providing third spaces for example (or whatever TW would choose for those spaces to be called) that meet their gender identity need and desire to not group themselves by or use facilities for their biological sex. It is not however possible to maintain respect for and inclusion for female people who believe in sex being binary however, if all female single sex spaces are rendered mixed sex and the gender belief being forcibly imposed upon them. In this sense, those female people are being required to validate a belief system they do not share in, with nothing less than their bodies.
And to those who believe in sex as a binary, this is quite simply sex based discrimination of female people being made to provide a non consenting service to male people who's feelings, wishes and choices are given considerably more care and priority than theirs.
Are you a fan of this kind of discrimination against female people to better provide for male people? And do you believe that having to choose between performing a belief not shared whatever the personal cost or losing access to any service is a fair choice to present to one, single, sex based group of female people? (For whom those facilities were designed and provided in the first place). Because I, emphatically, am not.