For people who have claimed for years that GC women are obsessed with toilets, TRAs who regard the Supreme Court judgement as suddenly undermining their right to use a toilet are pretty, ... well, ... obsessed with toilets.
The judgement has so many other, more important, ramifications.
Don't play their game. Whatever problems there are with men accessing women's toilets have been adequately dealt with by the SC clarification of the law.
Service providers, public bodies, and employers, can all feel confident now that it is lawful for them to provide single-sex facilities. What that means in practice is that if and when there are complaints about males accessing the toilets they can take appropriate action, such as warning that a gym membership will be terminated, and then actually terminating it if the person continues to break the rules.
Usually that will be all that is needed. But in cases where men are accessing women's toilets in order to harass and intimidate (as would be the case if they did it in the course of a protest action) I'm pretty sure that existing laws, such as behaviour likely to cause a breach of the peace, would enable police to take action
We have never had a culture in which service providers (etc) have pro-actively enforced single-sex spaces, In practice, this has always meant that a few passing transwomen will slip in. That's not likely to change, since the judgement has not created any additional enforcement duties for service providers etc. So TRAs are pretty much getting exercised over nothing. This is especially true given that as soon as you move out of particular bubbles, such as university campuses, NHS staff facilities, London hospitality venues, there really and truly still is near-universal expectation that women's toilets are for women, and there is also a near-universal co-operation with that. So nothing is going to change, except in those bubbles.
It is a non-issue. Don't make it an issue by proposing needless laws that will foster a victim mentality.