I've gone adventuring as a Changeling through lands in Eberron that are downright hostile to shapeshifters. My party included a warforged, human, and elf. None of us judged each other based on our races or sexes. Really, we let all our differences aside to further the purpose of showing a foreign diplomat around.
I like the morality that adventure groups promote: they're pragmatic. They don't encourage the group to love one another - My character was a cowardly poison using assassin, why should a warforged respect or love that? However, tolerance of one another is a realistic goal and allowed each of us to live in peace enough and learn to trust each other.
So when a group starts with, at the very least, tolerance of one another this can lead to further virtues like trust and loyalty. Really, games like Dungeons and Dragons are some of the best tools for teaching basic social virtues. I mean no disrespect to religious people, but reading the bible or having morality preached at you, I'm sure, instructs you what is virtuous and what isn't, but I can say the same of the Superman comics I read as I child (I really did learn to value truth and justice from these), but Dungeons and Dragons is an actual social experience where one must act out these virtues and learn to use them. The fun of the game aside, this is a valuable experience that puts the theory of virtues into practice.
If I ever have children I'm raising them as gamers. I really believe this won't just bring enjoyment into their lives but teach them valuable lessons.