> I think GP believes that race and orientation is mutable
Not particularly.
Race and gender are social constructs, and ones identity (and orientation, in the latter case) with regard to either is formed early – and, once formed, immutable or nearly so – as a product of innate traits interacting with socialization around the construct.
(The fact that gender identity can diverge from socially ascribed gender, resulting in demands to alter the latter to conform with the former, does not make gender identity mutable, in much the same way that the fact that people might mistake your race for a different one than your indentity doesn’t make racial identity mutable.)
I'll reiterate my previous comment then: the existence of detransitioners proves that gender identity is mutable.
From reading the accounts of detransitioners, gender identity seems to be more like a political or religious belief than anything else - often stable for long periods of time, but given the right circumstances, can be changed.
