I'm finding this discussion really useful, as I need to think through all the complexities of the implementation of the SCJ to be able to counter the arguments from people in the workplace and everyday life about how it's 'unworkable.'
It seems to me that we have a situation now where in shop changing rooms obvious looking men can be challenged and refused entry. This won't necessarily help with those few men who are very feminine and could pass, who people will be reluctant or unsure in challenging and will probably still get away with it.
There will probably be a period of TIM using not been challenged as a badge of honour for how gorgeous they are, and crowing over the 6'3 bloke who stuffed a bra being very upset he can't get away with it anymore.
Where I do think it will be different is in places where people reguarly use SSS such as the workplace. It is very hard to be stealth as trans in these situations, as often they've made a big song and dance about how brave they are, or there is online info they've shared. Basically they only way they could get away with it is if they manage to never reveal they are trans, which is very hard to do.
Once there is evidence they are trans, employers have a duty to ensure they use the correct SSS. If they continue not to, the employers will liable.
Basically a Sandie Pegg situation could never happen again.
So the SCJ does not mean that no man will ever be able to falsely access women's spaces unchallenged. That was never the case. Shitty very motivated men could always get away with shitty stuff.