That is not entirely true. The GRC is not a total matter of secrecy and can be disclosed for several necessarey purposes - such as in a police investigation. That overrides anyone not wanting to disclose. Quite rightly.
So for example in that awful rape of a woman by a trans person in a hospital last year they could indeed have esatablished if the patient had a GRC or not. Which I am almost sure that they did not in this case. But the decision not to find out for certain was incorrect. If they did have one then that could be disclosed to the police so it was simply chosen by them to not to pursue that option here or they were afraid to ask most likely given the way trans activists behave.
The person with a GRC can also tell anyone if you ask them and I cannot see any good reason why they would not if it mattered in the circumstances of any dispute. Being obstructive is the last thing we are seeking. We regard the GRC as a bond of trust with society. Not some ticket to do anthing we want.
If that person chooses to lie or declines to say then that is a problem they create and if it is assumed they do not have one by default then they have no reasonable comeback. The Equality Act advises people the can do that and it is perfectly reasonable to do so.
Those with a GRC are not like the trans activists out there. We are not looking for trouble or to cause a scene. If anyone challeged we would either tell the truth and / or just go elsewhere. The last thing we are aiming for is to be noticed.
Whereas that seems almost the only thing transgender activists are out to do.
Also not all of the 5000 have altered birth certificates as this requires taking extra steps but cannot be done without a GRC - so there are probably only about 4000 or so who have one in the UK and about a quarter of these are women who have changed their birth certificate.
Again here the original record is not removed and the link is retained to birth identity and whilst not made public it can be accessed for legitimate reasons. Including police investigations.
That is my understanding.