Bit late to finally catch on that they're losing their audience ratings.
Men with GRCs still exclude women from women's spaces where those women due to their needs and diversity cannot use mixed sex spaces - men's inclusion isn't more important than women's, either inclusion matters or it doesn't. If it's ok to just bump women out of anything so men get their comfortable happy choices then it's male supremacism, not inclusion. Let's be honest about this and discuss whether as a society we agree that women are a subclass with less rights than men and we're all ok with this.
Women have freedom of belief: not all women perceive men with GRCs as women, and are entitled to single sex spaces. Women who do share this belief are welcome to go and use mixed sex spaces, good for them, but they don't get to remove rights and facilities from other women on the basis of belief.
Having raped or worse is no barrier to getting a GRC, and any chancer can get one and then harass and harm women at will in women's spaces.
No one can ask to see a GRC or check, women's spaces mostly aren't gatekept, so in reality if any man can walk in under any pretext then all men can and must be assumed by the act of walking in that they are declaring themselves as having a GRC. (As some women are forced to walk out and cede all access, and the other women start hoping that the man does not decide to harass or hurt them today - it's in his gift, it's his decision, not theirs.)
Making it men with GRCs only still does not work for women. Third spaces would by providing access for all, and would need to come with heavy pressure from all parts of society that men have to respect women's equality of access needs and make it clear that only an unfashionable bastard would not do so or exclude women, and that society will shun and be disgusted by men who treat women in this way. Get cracking Stonewall. Some nice shiny posters and school campaigns and employer courses and gold stars will do it easily.