The problem with "cis" is very clear from the page that OP linked to, which seeks to explain what being trans is all about.
From the Gender Identity Research and Education Society (GIRES) link that OP provided to explain to all of us silly wimmin why we're wrong to think that transactivists pose a threat to the aims of feminism:
"Male and female characteristics depend on two factors: sex and gender.
‘Sex’ describes our physical structure... There are two different aspects to gender: ‘gender identity’ describes the inner sense of knowing that we are boys or girls, and later men or women; ‘gender role’ describes how we behave in society. Even though we now live in a more equal society, boys and girls are still expected to dress differently from each other and, possibly, enjoy different kinds of games. Each is expected to have rather different interests and different groups of friends.
Typically, sex, gender identity and gender role are consistent with each other... As soon as the sex of a baby is apparent, it is assumed that the gender identity matches.
However, people vary greatly and it should not be surprising that, occasionally, a few individuals experience a mismatch... The way they are expected to behave may be quite different from the way they actually want to behave. This causes a feeling of intense discomfort which is described as ‘gender dysphoria’ (dysphoria means unhappiness)."
The fact that organisations like GIRES are pushing the narrative that "occasionally, a few individuals experience a mismatch" between their biological sex and the way they are expected to behave based on their gender role , basically accepts gender roles as legitimate, inevitable, hand immutable.
Do trans activists really think that it's only "a few people" (those who think of themselves as "trans") who occasionally feel extreme dissatisfaction and discomfort from gendered expectations? Do they not realise that the old name for being dissatisfied with gender roles was "feminism"?
If trans support and education websites are saying that trans means "discomfort with the gender role attached to biological sex", then what might a "ciswoman" be? A woman whose biology happily matches her cultural 'gender role' and who experiences no discomfort nor dissatisfaction with having a sexist society impose assumptions and expectations about her behaviour, her interests, her abilities, her friendships? Because that ain't me. And it's not my mother or my sister or (God forbid) my daughter, and it's not any of the women that I know either.
If someone expects me to deny my own biology and/or my own personhood outside of bullshit sexist gender roles, and be complicit in the blatant disrespect that this trans narrative displays for women's centuries-long struggle for equality and freedom against gendered expectations, by referring to myself or anyone else as a 'ciswoman' well, sorry, no. They can fuck. right. off.