"I see this widely repeated but I cannot find an authoritative source (like case law)"
That is because, as far as I'm aware, there is no case law on that particular point.
Indirect discrimination does definitely require a person to hold the particular PC:
19 Indirect discrimination
(1) A person (A) discriminates against another (B) if A applies to B a provision, criterion or practice which is discriminatory in relation to a relevant protected characteristic of B's.
(although section 19A does say that there can be cases where B does not have to actually share the same PC).
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In contrast, direct discrimination just uses the phrase "if, because of a protected characteristic"
However, if you look at Section 13(3) there is an exemption for disability:
(3) If the protected characteristic is disability, and B is not a disabled person, A does not discriminate against B only because A treats or would treat disabled persons more favourably than A treats B.
There is a similar exemption in subsection (6) for women in connection with pregnancy, childbirth or maternity.
In contrast, there is no similar exception for gender reassignment. There is no part of the Act that says:
If the protected characteristic is gender reassignment, and B is not a person with gender reassignment, A does not discriminate against B only because A treats or would treat persons with gender reassignment more favourably than A treats B.
The lack of this exemption would suggest that GR is a different kettle of fish to disability or maternity.
But that would, no doubt, come down to statutory interpretation again.
Do you really want to consider a case that may go to the Supreme Court?