A transwoman who has bad intentions can make a woman’s space unsafe, so can a woman who has bad intentions.
I think the main issue is down to how a transwoman using the facilities would make a woman feel, which is perfectly valid. Obviously we should not just accept that woman may feel uncomfortable with no questions asked but then as it does regularly come down to ‘so what if a transwoman feels uncomfortable in the mens’ is there not an element of ‘my feelings matter more’ underneath it all?
No its about the fact that single sex facilities are needed for girls and women's safety, privacy and dignity.
This was the basis on which they were fought for.
Here is an interesting piece of historical study:
'Sexism in the "Bathroom Debates": How Bathrooms Really Became Separated By Sex'
Yale Law & Policy Review, Vol. 37, No. 1, 2018
by W. Burlette Carter
Abstract
This article challenges two widely-embraced theories about how public intimate spaces (e.g., toilets, locker rooms, showers, etc. hereinafter called “bathrooms”) first became separated by sex. The first challenged theory claims that the very first instance of sex-separation in public bathrooms occurred in 1739 at a ball held in a restaurant in Paris. Under this first view, sex-separation first emerged as a sign of upper-class gentility and elitism. The second challenged theory argues that a consistent practice of differentiating bathrooms by sex did not emerge until the late nineteenth century. According to this view, bathroom sex-separation was imposed when authorities overreacted to the notion of the intermingling of the sexes as women entered the workplace during the Industrial Revolution. Thus, the second view holds that bathroom sex-separation is rooted in sexism, paternalism and outdated Victorian notions of modesty.
This article provides evidence to show that, while widely embraced by media, both of these theories are wrong. The author traces the 1739 Paris ball to its origins (a ball celebrating the wedding of the daughter of Louis XV), and demonstrates that scholars misinterpreted that event. Moreover, she demonstrates that bathrooms have long been separated by sex, and that the primary reason for that separation was securing safety for women and children in an atmosphere of harassment. Indeed, the sex-separation laws that emerged during the nineteenth century labor movement were among the earliest anti-sexual harassment laws in the nation. They did not fail because they sought to protect women; they failed because they did not secure similar protections for male-bodied victims. At the same time, the author argues that some lower and middle class sexual minorities and others sometimes wanted or needed different rules. She theorizes that a common "safe space" was the masquerade balls. But even when they created such spaces by consent, and adopted intimate space approaches to suit their needs, authorities later forced them to abandon these approaches. Seeking to preserve their power positions, upper class sexual minorities may have cooperated in these suppression efforts.
Historians erred in recounting the history of bathrooms because they misunderstood the language of earlier eras, they failed to sufficiently consider women's history and they ignored the condition of the poor. Thus, as they propose an explanation of sex-separation that advances the interests of some sexual minorities, they offer a narrative that oppresses women and the female-bodied generally, especially those in the middle and lower classes. Such histories erase evidence of women's historic struggles with sexual assault and sexual harassment. They similarly ignore the struggles of the poor for safe intimate spaces.
Women and others must push back on approaches that contort women’s history. They are rooted in sexism and patriarchy, even when they may be intended to advance freedom for other groups."
papers.ssrn.com/sol3/papers.cfm?abstract_id=3311184
and a very informative speech about toilet design by a UK expert:
Professor Clara Greed, WPUK Bath, 1st November 2018
www.youtube.com/watch?v=aD92aLqgtTA
www.mumsnet.com/Talk/womens_rights/3427591-WPUK-Bath-fascinating-important-speech-by-Clara-Greed-Professor-of-Inclusive-Urban-Planning-specialist-in-toilet-provision-with-particular-emphasis-upon-womens-needs