YANBU to take an interest and have these concerns, but having read the only details of the bill available so far (it's a private members bill so takes longer to be published in full), I think YABU, as I don't think (hopefully) that the bill will do that.
The records of the debates so far state that:
"Mrs Maria Miller, supported by Jess Phillips, Mrs Flick Drummond and Ben Howlett, presented a Bill to make gender identity a protected characteristic under the Equality Act 2010 in place of gender reassignment and to make associated provision for transgender and other persons; and for connected purposes."
So it's replacing "gender reassignment", not "sex" on the protected characteristics list.
Still something to watch carefully though, as "gender reassignment" is clearer - you will have had to go through the full process to be a protected characteristic. "Gender identity" is, as you've pointed out, more fluid and could lead to difficulties.
Also, don't forget, this is the equality act. So it sets out what you can't discriminate against. Whatever exemptions existed before to allow discrimination in certain circumstances (i.e., I don't want a male carer, it has to be female, which on the face of it, is discriminatory) would continue to exist, so you are mostly talking about situations where the act wouldn't apply anyway.
You can follow the progress of the bill and read the debates on it as it becomes available here
services.parliament.uk/bills/2016-17/genderidentityprotectedcharacteristic.html
Hope that's some comfort to you OP