What is it about gender reassignment being a PC that you think takes away from other people?
Well, there is a huge list if you want to go down that route but mainly due to misinterpretation of the meaning of "sex" in the Equalities Act.
Women's Sport has already been mentioned. Then there are all the grants, awards, prizes, employment and political opportunities designated for women in order to encourage participation of women in male-dominated areas.
Men who call themselves women taking away the dignity, privacy and safety of women who need same-sex accommodation or care.
However, what we were actually discussing was that a "catch all" PC of GR unnecessarily privileges someone with the PC of GR who is actually being only discriminated against on the basis of, for example, Sexuality (homophobia).
Compare with a pregnant lesbian with a disability who might rightfully need to claim, and prove separately, unfair discrimination on the basis of:
- Sex
- Sexuality
- Disability
- Pregnancy
There is a presumption of intersectionality inherent in the PC of GR that in practice might be totally irrelevant, ie. the "distinct vector for discrimination" that you posited earlier.
Meanwhile, actual intersectionality, which was intended to address the dual discrimination affecting Black women in the USA, is not addressed for anyone covered by the other Protected Characteristics.
The PC of GR treats some people as a special sort of human unlike any other.
Firstly, no, they are not.
Secondly, "trans", and therefore the PC of GR, covers a completely heterogenous mixture of characteristics and people.
There is no commonality between, for example, a pre-teen girl distressed by the onset of puberty and wishing she was a boy and, for example, a middle-aged to elderly man who has decided to "transition" from being a weekend transvestite in fetish clubs to "bringing his whole self to work" as an occasional to full-time cross-dresser.
That is is where the "shoehorning" comes in, ie. in the creation of the PC of GR.