A more effective form of transallyship would be to reassure any apprehensive transpeople that they are in fact being manipulated into groundless fear by a form of activism that isn't genuinely in their interests. The guidance simply clarifies the existing legal situation, and leaves us exactly where were at the point when the equality act was passed, before 'stonewall law' muddied the waters.
There are no additional sanctions for trans-identified people who access opposite-sex facilities, there will be no additional monitoring at toilet doors. In all probability, the minority of trans-identified people who slip through into the wrong toilet will still be able to do so. And in all probability there will be pockets of blind-eye-turning to this behaviour, as there have always been.
The key difference is that facility providers will no longer feel permitted or coerced to mis-state the rules of access. That will make it much easier for the 'social contract' of unenforced near-total compliance to reassert itself. Abusive trans-identified males will feel less emboldened to exploit single-sex places for voyeurism, exhibitionism, harassment, etc.
Paradoxically, that will make it easier, not harder, for the odd 'passing', non-abusive trans person to do as some of them have always done and slip in to the wrong facility - because women will be able to stand down from the enhanced perception of threat that illegal trans-inclusive policies had generated.. I'm not making any statement about whether that is a good or a bad thing. I'm just observing that it will continue as it always has, so these people won't be worse off.
And as for the concern in the petition that some women might suffer additional problems accessing women's spaces based on their appearance, whY should that be the case -- given that (even during the height of "stonewall law") we have always had single-sex spaces and in most parts of the country most users would have understood single-sex to mean single sex? Why, also, would this be the case given that the guidelines don't materially change the level of enforcement or monitoring levels required?
If there has indeed recently been a greater willingness to challenge women-who-do-not-look-like women (which is far from certain), it seems fairly obvious that that is because, until the SC judgement, we were hearing false claims from all corners that men were allowed to come in on their own say-so. Now that lie has been nailed, any women who have recently been challenging people in toilets will be able to reduce their vigilance and we will go back to normal