@neil @feff @mindpersephone (Non clinical NHS Wales employee, not speaking on behalf of any part of NHS Wales, part of my health board's queer working group)
You're right about gender being less relevant but for simplicity we use gender markers.
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Context and details: For NHS Wales, gender is an important marker (and age) because that's how we define the default inclusions for screening everyone (according to your GP record)
For trans people, you will by default be invited to get the same screening as your gender. You would then need to opt in and out of the appropriate screening based on your AGAB
(More info here: https://phw.nhs.wales/services-and-teams/screening/information-for-people-who-are-transgender-or-non-binary/)
GPs should be having a discussion with trans people when they change their gender marker if they're following https://www.gmc-uk.org/professional-standards/ethical-hub/trans-healthcare to cover screening and the alike
For then any other trans specific healthcare, that's handled by CAVUHB's Welsh Gender Service with dedicated experts to best support those people https://cavuhb.nhs.wales/our-services/welsh-gender-service/
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It's one of those things which prob should be better handled with forms like GMS1W (form for joining a GP permanently) which still only have male and female markers on them.
Outside of non-binary markers, some do argue that it may be better from a confidentiality and equality view that only relevant bodies know of someone's trans status which does change how they provide that care, and otherwise treat trans men healthcare in the same manner as any other man (because they're men) with any medication in the same manner as regularly prescribed medication
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That's a lot of text to describe why and hopefully that helps in some way, advocacy groups are pushing to improve this sorts of problems. One can hope it gets resolved soon.