You just want it to be true even though you have no idea what goes on in a person's private thoughts. Kids are influenced more by popular culture than they are by their parents. There's a ton of pressure to conform to this diversity is our strength mantra. Once they get out into the real world, then they're likely to develop opinions of their own.
I don't need to want it to be true. I never thought about the race/religion of my friends because I grew up in a diverse neighborhood. if you were a bigoted ijit, you were probably pretty lonely in Brooklyn.
and no, I rasied my son in a diverse environment, too. he's been around too many decent people of every stripe, and too many cruddy people of every stripe to give a damn about what they're born.
you should try it. you might be happier. and maybe you'd no longer be trash.