This is not quite the same, in my view, as, say the Lesbian and gay movement, although I have read that being argued online.
For instance, I have read that 'cis' is just the same as introducing 'heterosexual' or 'straight' to allow gays and Lesbians and bisexuals to have their sexual orientation treated equally with the majority.
But 'cis' is not the same thing, because it orders people to believe in an abstract gendered soul which may happen to match the sex of their bodies or not. Most people don't share that belief for themselves, i.e., they don't feel an abstract inner gender identity.
So being told to use 'cis' is not like being told that the opposite-sex sexual orientation is called being heterosexual. The former changes the meaning of the phenomenon discussed by erasing the possibility that many people don't have gender identities at all or that their identities are embodied, based on living in a sexed body.
So what is being pushed and pulled here includes the way everyone is expected to define themselves, even if the demanded changes invalidate most people's actual self-definitions and, in some interpretations, would replace those with deeply sexist and retrogressive new definitions of women and men, say.
I don't think this is the usual type of language change at all.