You know what? Yes; the push for equality for transgendered people is an effort to change a social norm, in much the same way as efforts at Integration in some areas were designed to change the norms there, too, of "coloured seating,"coloured schooling," and "coloured housing."
But that isn't meant to "upend society" - whatever scaremongering horseshit he means by that - but rather to ensure that all rights are recognised and universally applied.
In the disability community, there is a term called, 'the Right to Risk' - meaning that if a (primarily physically) disabled person at the age of majority wants to go base-jumping, for example, no one should be legally permitted to stop them; their disability doesn't render them unfit to choose if they want to engage in risky sports, risky sex, or any other activity an able-bodied person may do. It might surprise some of you to learn there's a too-large-for-my-taste minority who will, without permission, grab a blind person by the arm while the two are merely standing on a train (with the assumption being the sighted person could help the blind one debark) or take the handles of someone's wheelchair to push them up a ramp but entirely unasked. It's troubling and dehumanising, and it's fucking condescending as well.
When people are told to remove their hands, some become defensive or even hostile (e.g., 'If you don't want help, and insist on pretending you can get along without help, don't be surprised if you fall off the platform someday where your pride will kill you' - and that was damned near verbatim for what one idiot said) because they were allegedly just trying to help. It's shocking how many people think, "I just wanted to help" is a good excuse for treating the body of a total stranger as some species of public property. (Women, too, had - and sometimes still must - to fight for the right to take risks.)
And it never dawns on those who do paw disabled people, then feel martyred because their "good deed' told them to fuck off, how they themselves would feel if grabbed while blind or grabbled from behind while using a wheelchair.
Anyway, most people prefer a certain amount of law and order, so the majority of those who've given this any thought aren't out to "upend society." They're out to advance it beyond stone, bronze, iron, or even the space and information ages, into the next age...the one where we either work together or destroy each other.
Those are the only options we have at the moment: Broad cooperation, or human extinction.
But if a society is such that it's okay to make people of different races drink from different fountains, where it's okay to treat adults like children because they're missing one of the five senses (etc.), where it's okay to turn private sexual decisions into a public spectacle, then, yes; upend society.
Rebuild it on a foundation of respect for the dignity, autonomy, legal equality, privacy, and basic human rights for all persons.