Gen X, Gen Y, and Gen Z are all fine as labels and nouns, especially when used symmetrically.

GenXer, millennial, and GenZer -- when juxtaposed as such -- are showing a lack of respect and lingual parity to members of Gen Y. Sometimes, but not always, this may be accompanied by a person's animus toward the Baby Boomer generation ("Ok, boomer"), as you alluded to earlier.