I think what will change is womens ability to complain about an obvious man hanging round in the womens loos.
Men can say they are transmen now, but passing transmen do not use the ladies. So unless this guy who is saying he is a transman looks female, then that excuse will not wash.
I really see no need to change how things are now. What need IS there? 
I have a transsexual family member and she cannot see what the need is either. This whole 'self-ID' thing is silly. She says anyone who is transsexual can get a GRC under current rules anyway, as they have sex dysphoria and will be having treatment so will be able to get the medical declarations, so this 'it will make trans peoples lives easier' does not wash.
Personally I see no need for the GRC anyway. The reason for it was so that transsexual people could marry someone of the same sex (it came in before equal marriage) and for pension rights. But both of these are rectified now, so the original reason for GRCs is moot.
Things are fine right now, with the honour system that women have going on for sex segregated areas, surely. Even in changing rooms, women turn a blind eye to transsexual people (if they do not pass, not many do, if they pass then there is no issue at all as noone knows) but would complain if there was an obvious bloke there. What exactly is wrong with this? All this self-ID stuff will do is force women to be uncomfortable, or stay at home as that pervy guy could follow you in and you cannot complain. It will also be detrimental to transsexual people, who currently use female areas to escape that pervy guy. As he can follow them in also.
This 'transmen' thing is a bit of a red herring. As I said passing transmen already use male areas as they are women and know that their presence in a womans area would make women uncomfortable as they would be read as male.