The point is I could challenge any male in a female space right now because I know they are very unlikely to have a GRC. The fact that a GRC is offered to a much wider group means there will be more males accessing our spaces either under that process or outside it.
A lot more males and we would have way less recourse to challenge them.
Not just less recourse to challenge them, but you will be found guilty of a hate crime and punished accordingly, if the person can legally 'prove' that they are a 'woman'.
At the moment, a 'normal' transwoman, with no deliberate intent to do women any harm, could use women's single-sex facilities and, other than making women feel fearful and unsafe in using their own facilities, nothing horrendous (tangible) may come of it.
There will of course be that huge feeling of invasion - one which all decent males (whether transwomen or not) would obviously be aware of and, you would expect, would respect women's right and wish to have single-sex privacy and thus not invade - but some TW may be so wrapped up in their own little worlds that they somehow (initially) don't appreciate this.
With a GRC, the transwomen who DO intend women harm (or at the very least get off at the thoughts of their discomfort) can completely turn the tables on women, make them into the bad guys, themselves into the poor defenceless victims and, if they so desire, report those women for hate crimes, transphobia and anything else they want to try to stick on them. The same person who knows that they are making women feel unsafe by appropriating their single-sex spaces can then claim that those women are then making them feel 'unsafe'!
Put simply, they would have both the protections of being 'women', just like any woman, when it suits them; but also the protections of being transwomen, when that is more expedient. It's the same story of TRAs using the false pretext of transpeople having fewer rights than others in order to wrest more rights for themselves directly from other groups (i.e. women).
To simplify it even more, imagine that everybody is legally allowed to certify themselves as not-guilty of any serious crime. For the vast majority of us, this will make no difference at all - because we are not-guilty of serious crimes. The only minority that will benefit from this change in the law are the very ones that no right-thinking person would want to be able to benefit from it. However, nobody will ever even know that they have escaped justice on a technicality - because they are considered by default legally to be in exactly the same situation as all the rest of us wrt committing crimes - and in fact, it would actually be hateful for anybody to even mention their obvious perception of gross unfairness at this.