The most upvoted comment under the article is one complaining about the lack of public toilets, but the second-most upvoted says this: (I've not quoted the entire comment)
A more useful distinction when it comes to toilets is between biological men and biological women. Men like to wee standing up, so urinals are useful. Men don't usually want to be observed weeing by women (and neither do women want to see men weeing) so that's one good reason for segregating by the sexes.
Another good reason for sex segregation is that biological women menstruate, and like to have some privacy for, for example, washing blood-stained hands or rinsing a moon-cup. This is particularly true for young girls, who can start menstruating as young as nine or 10. It's cruel to force them to deal with that in toilets also used by men.
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Toilets segregated by biological sex have served us well for a long time, the main problem being that there aren't usually enough cubicles in the women's toilets. If you address this, and you have a few nice large cubicles for people with disabilities, then there isn't much more you need to do. You certainly don't need to introduce "gender" into it, cisnormative or otherwise. Gender isn't important when it comes to toilets; biological sex is.
Which seems sensible to me.