One premise of Lennon's song Imagine is that without religion the world would have fewer between group conflicts. Over the long run, I doubt it. Humans will still find ways to form cliques and credibly signal allegiance to their cliques by denigrating other cliques in irreversible ways.
Look at the evolution of educated society's morality standards. Moralizing about other's sexual tendencies used to be the high status way to signal superiority. But hitherto oppressed groups with non heteronormative tendencies convinced educated people that this was an unfair practice. Yet, educated people still find ways to signal their superiority! For example, they now often do so via their preferences for certain types of food.
So, here is a short list of issues in which I believe an elimination of diversity would not reduce the amount of between group vitriol, following perhaps a short adjustment period: geographical origin, race, ethnicity, political party, sport team affiliation, attractiveness, and religion.
If you are not a nihilist in general and wish to remain consistent, the salient question becomes: towards maximizing which qualities should we nudge the inevitable human status competitions?