The proposal fails on many counts.
Not only the 'outing' but also because post transition transsexual people can get their passports and driving licences changed anyway without having to have a Gender Recognition Certificate. All they need is the psychiatrist's letter and current documentation (such as birth certificate etc). So they don't need the ID card.
Now if she meant trans gendered people who vary their gender on a day to day basis they couldn't have an ID card in their alternative gender anyway.
So this proposal was based upon stupidity, ignorance and desperation. Fairly typical of that lot.