The Court of Justice of the EU has ruled that under the GDPR, the asylum documentation of a refugee in Hungary must be corrected to reflect their identified gender (as opposed to assigned-by-government gender). There are some caveats to it however.

While evidence of its correctness may be expected to process the change, that evidence requirement *may not* include having undergone gender reassignment surgery, as this would be in conflict with the European Convention on Human Rights.

A major factor in the ruling was that the refugee was granted asylum on the basis of being trans in the first place, and this served as an implicit recognition by the government that their identified gender is correct, from a GDPR perspective.

The full details of the ruling are here: https://gdprhub.eu/index.php?title=CJEU_-_C-247/23_-_Deldits&mtc=today