Love the idea! Everyone has something in common, as long as we keep this in mind and look for it.
Start with people who are not your friends yet: Share your stories, interests, hobbies, passion, etc. I am sure you will find more commonalities than what you expected.
So simple, yet so true. Just seeing and sharing this design with others, I think, has a positive effect.
Next time I'm angry at or in conflict with someone, I'll try to remember that we're all human, and consider our commonalities.