I chose the service station toilets example quite deliberately. In that environment nobody is going to conduct any ID checks. Those spaces are protected by social norms and taboos. My concern over self ID in that context is that it emboldens men who have no intention of making any effort to pass to go in and intimidate women, and dare anyone to challenge them.
Other situations need different approaches. In female spaces where nudity or semi nudity is expected, GRS is more important than a GRC. Unlikely that you would notice a trans woman in the showers following GRS. Not sure how you are going to police any attempt to keep them out.
Refuges can make checks. They could ask to see a birth certificate or a mechanism be set up for them to check the register of births. That wouldn't be an issue for me. Even with a GRC, I would never seek to use one without making it expressly clear that I was transsexual. But self-ID makes it harder to screen out those with a GRC.
As for bursaries, scholarships and benefits targeted at females, and all women shortlists, they should check someone's sex in order to prove that they have discriminated legally. But hell would freeze over before I took any of those places from a woman.