Yes of course some men take any opportunity to abuse girls. Just look at the awful stories of the physio in US Gymnastics.
That's not the situation here, though. It isn't saying 'you have to flash your bits to whoever wants to see them' (step this way, abusers, the door's open) It's saying 'we need evidence that children are playing in the right teams. So get an HCP to provide a note which could be evidenced from long term knowledge of the patient, a cheek swab, a blood test, or... if all of those things are somehow impossible... an examination.'
If you have problems with doctors seeing genitals then we have a major problem, as it is often a medical necessity and we generally trust them to do this appropriately.
If an HCP is an abuser, then that is another issue.
I don't think this calls for strange men to turn up with 'genital inspector' badges and insist on private examinations.
Consent would need to be given, a parent would need to supervise and if all of that was deemed too traumatic, then one of the other options could be taken.
As it happens, most family doctors know their patients well enough to sign off on biological sex without any tests at all.
The only grey area would seem to be where a child actually is transitioning, in which case a doctor would be even more likely to be fully apprised of that fact and could declare such without any examination at all.
I don't see this being more problematic than women having smear tests. We don't shout abuse about that.