Radical feminism is a militant form of feminism. One of the tenets of radical feminism is the promotion of women-only spaces. Some radical feminists understand this to mean women spaces for ALL women (cisgender & transgender), while some other radfems see trans women as interloping men. This second type of radical feminists are described as trans-exclusionary, which gives us the acronym TERF (trans-exclusionary radical feminists). A typical example of this is Germaine Greer.
To your second point: I find it odd that you’d be triggered by hearing “cis privilege.” Let’s unpack that.
So… “transgender” means “across + gender” — meaning something like, “when your gender and your biology are not so much aligned, as away and across from each other.”
The opposite of transgender is, what…?
The answer many folks give is “normal.” The opposite of transgender is “normal.” Do you see how this would be problematic? How this obviously makes us “abnormal”? So, in the spirit of kindness, someone coined a word that represents “not transgender” — that word is “cisgender,” (cis=next to, or aligned with+ gender) — meaning something like “when your gender and your biology are aligned with each other.”
Cisgender has no insult in it. It’s just a word.
While we are usually uncomfortable contemplating our privilege, it’s a worthwhile exercise. I have White privilege. Cops usually are polite to me. I have ableist privilege — my mind works decently well, and my body works decently well. As a trans woman, I am now experiencing ‘passable’ privilege — I can blend in, which gives me added safety and comfort.
Cisgender people have privileges trans folk do not have. They do not experience gender dysphoria. They do not go to massive amounts of job interviews, only to be told they’re “very impressed with you” but they’ve “decided to pursue another candidate.” It does not cost them thousands of dollars just to make their bodies display a relatively acceptable portrayal of their gender. They’re not gawked at. Etc.