This is not SG's fault. I'm not saying that to defend her - I'm completely opposed to everything she stands for. My point is that this is all on the Tavi.
It's actually not that unusual for NHS services to accept referrals from non-medical sources. Generally that's a good thing - if, for example, a school has concerns about a child's mental health, it makes sense for them to be able to refer for support without involving the GP, if the GP does not know the child well. Likewise with expert charities.
But, for all referrals, whether from an HCP or not, the clinician who receives the referral is responsible for managing it appropriately. Even a GP will often refer to the wrong service, because services are constantly being reconfigured (if you read Hannah Barnes' book, you will see how much confusion there was between the Tavi and the gender endocrinology service, even amongst expert professionals). So every referral needs to be sifted, to check that it has reached the appropriate service, and that the request in the referral is appropriate.
This is what went wrong here: not accepting referrals from non-HCPs, but failing to manage them appropriately, and GIDS allowing themselves to be pushed around by Mermaids.