So what precisely makes a TW a 'woman'?
A woman in UK law is a female of any age.
A man in UK law is a male of any age.
No one born female can be a TW and no one born male can be a TM.
A TW is a male with the protected characteristic of gender reassignment, a TM is a female with the same protection. Unless they have a GRC, they remain their legal birth sex.
The only thing that makes a TW a 'woman' in UK law for most but not all situations is them having a GRC. Exceptions apply, for single-sex spaces, even with a GRC.
So if a TM, a female without a GRC but with the protected characteristic of gender reassignment, is discriminated against by a woman only service designed for females, then yes, it seems obvious "the comparator would be another woman without the protected characteristic of gender reassignment, with the claimant alleging discrimination against them because they have the protected characteristic of gender reassignment."
So, for example, a TM without a GRC fleeing from violence and wanting to access a Women's single-sex refuge should not be discriminated against based on their gender reassignment, as their comparator is other females without the protected characteristic of gender reassignment.
But on what grounds could a TW, a male without a GRC but with the protected characteristic of gender reassignment claim to be discriminated against, if they were attempting to access a service designed for females only? On what legal basis would their comparator not be another male? Bobbins indeed.
Anyway, this is why the Belfast case is so important.
The judge rejected the idea that a TW without a GRC is a woman. They are not.
Difference in treatment between the two is 'objectively justified'.
TW (without a GRC) ANW.