Not sure this particular expression of gender critical belief has been set in a legal judgment, so it may not be possible to legally challenge it
Well, they'd have to refuse to consider your application first. Presumably you'd hit the crunch when you refused to tick an "identify as female" box.
If they refused to consider the application because you refused to say you "identified as female", then it would be clear direct discrimination on belief, because they would have considered another woman who did not refuse to "identify as female". Requiring you to "identify as female" to get a job is a belief test - such things may be permitted in some circumstances, but much more limited than the sex exemptions, and almost certainly not relevant to this job.
Also, if they refused an application from a transman, at least without a GRC, whether or not they "identified as female" that would be discrimination on the basis of gender reassignment. If the transman didn't "identify as female" it would be indirectly discriminating on the basis of gender reassignment, as they would have considered (genderologist) women who do "identify as female".
If the transman had a GRC, then it's above my pay grade.