This is going to sound stupid, but one day I was talking with my ex-friend “Carol”. While we were friends, someone said the word “heterozygous”. Carol mentioned that she was straight, so I jokingly said "hetero, like you, Carol!’
She acted as if I called her a slur and got very offended, saying “How dare you call me ‘hetero’?!” so I apologized.
(We are ex-friends because of drama [not this], which is kind of a long story, but I guess not the point of the post.)
I have heard many straight people call themselves “hetero”, though, including myself when I thought I was straight.
Far as I can tell, the sort of people who think “hetero” is a slur (or “cis” for that matter) are bigots who are offended by the thought that non-cishet people even exist.
I still get a twinge from cis, but I put that down to unfortunately spending too much time around people who actively used it with the connotation of a slur.
I’m still trying to get over that twinge.