How the GRA and EA2010 interact has not been properly explained at all and can't be until sex falsification of documents is ended.
I think this massively overstates the significance of sex-stating documentation. For one thing, in a number of frontline situations (the changing room at Primark for example) it would never have been practical or realistic to resolve the situation on the basis of documentation being provided. Can you imagine a fitting room attendant ever doing this, even in the days before people could change their sex markers on docs? In these situations, documentation is a red herring. The fitting-room attendant would simply call the security staff, who would escort the individual from the store. And thanks to the new guidance their employer could feel confident that (provided they had followed their own procedures properly) a civil challenge by the excluded person would not succeed
For another thing, in cases where it might be realistic to ask for documentation (such as intake at a refuge), the law has clarified that providers can consider the normal range of evidence in front of them regarding a person's sex, including their behaviour and the concerns of anyone involved. They aren't required to use documentation as a criterion for determining sex, so it doesn't really matter that documentation is an unreliable determinant of sex, except in the genuinely tiny number of cases where all the other evidence of sex (appearance, behaviour, concerns) is moot
Also, I think the concerns about documentation misrepresent the ways in which a 'challenge' would occur. In many cases, it wouldn't be a simple one-off moment of challenge. It would be a civil matter in which a person accessing a single-sex facility is breaching the terms under which they are permitted to be on the premises. The provider could then take action to get them off the premises.
As will all civil matters, the police may not be able to become involved (unless the individual is also suspected of breaking criminal law - eg threatening behaviour, sexual assault). But providers encounter this sort of situation all the time (in contexts unrelated to enforcing single-sex facilities) and devise systems to deal with it. For example, imagine a gym where someone is trying to use the equipment but their direct debit has bounced so they haven't paid their membership fee.
Access to my gym is by means of pressing a smart-tagged bracelet against a reader, which opens a turnstile. If someone was abusing single-sex changing rooms or failing to pay their membership fee, I would expect that, under the terms and conditions of membership, these are grounds for terminating their membership, which would result in their bracelet simply being deactivated.
In different contexts, other procedures and security measures may be appropriate. But the point is that providers aren't likely to be relying on a receptionist or similar 'holding the line' by means of a challenge, much less a challenge to provide documentation.