I have spent enough time studying these generational labels and stereotypes to find this generational warfare not only contrived, but as irritating as hell.
No generation is a monolith. We must consider two things. First, the ways in which "generation" intersects with race, gender, dis/ability, sexual orientation, class and other facets of identity.
Second, we should not ignore who creates, broadcasts, and uses these generational stereotypes, and for what purposes. They were marketing terms before they were identities. That is how consumer culture works. Once a stereotype permeates popular culture, it can be used by individuals to construct their own identities, or to "other" vast sections of the population. It can also be used not only to sell things, but to promote political agendas.
How is generational resentment any different from convincing people that Black people took your spot at the university, or that immigrants stole your job?