In my experience, people who object to the word "cisgender" practically always have very strong ideological opposition to the public existence of transgender people. They almost always actively spread lies about trans people, such as claiming that trans women are likely to be violent or that trans men are "failed lesbians" who capitulated to the patriarchy. (As an aside, this type of person doesn't typically seem to know what to make of gay trans men, but that's another story.)

Cisgender is, as you say, a convenient way to say "not transgender." People who have a problem with the convenience actually have a problem with trans people.