‘Functionally the same’
Bollocks is it.
Gender reassignment is a one-way protection (not everyone has the protected characteristic of gender reassignment)
Sex is a two way protection (everyone has a sex).
According to Genderism Gender identity is a two (or more) way thing - everyone supposedly has a gender identity, and those of us who deny experiencing such a thing are automatically designated ‘cisgender’.
Thus if ‘gender identity’ were the protected characteristic instead of ‘gender reassignment’ those of us who are ‘cisgender’ would automatically have gender identity based rights too. It would be a two way protected category, like sex.
So we could then divide services and spaces into cisgender and transgender, and then again by sex. This would put ‘transgender women’ into the ‘trans gender identity’ & ‘male sex’ categories
Whereas us boring old fashioned women would be in the ‘cis gender and female sex’ categories.
Male people with a trans gender identity certainly wouldn’t be entitled to spaces for female people with a cis gender identity, just as male people with the additional protection of gender reassignment are not entitled to spaces and services for female people.
HTH.