I’m only going by what women repeatedly say, loos are a safe space and they don’t want that altered with access to anyone in that moment when challenged saying they identify as a woman.
Women have spoken, generally they don’t want a free for all of those claiming to have identified as a woman entering female toilets. Covered in depth on R4’s (unsurprising) Woman’s Hour, for example.
The only solution I can see is shared gender neutral loos (each an individual room).