The answer here for me is that if she uses the women’s restroom, she’s putting other biological women in an awkward spot where they’re in the bathroom with a biological man.
If she uses the men’s restroom, it’s likely more awkward for her as the transgender person but it’s not like she’s never been in men’s restrooms. I can see how that would be awkward for her now that she believes she’s a woman, but that awkwardness is at least resting with the person who made the decision to change their gender and not with unsuspecting others who are forced to play along.
So for me it comes down to, someone is going to be uncomfortable either way, and it comes down to whether you’d rather make random females play along with her gender identity or if you’d rather make her play along with her birth sex.