Maxperson
Morkus from Orkus
Using your analogy, and attempting to explain what appears to be @Shasarak's view that you just don't seem to be getting:
Not eating liver because you don't like the taste makes perfect sense. I don't eat liver either, interestingly enough.
But when you say "No dragonborn at my table." it doesn't sound like you are saying "No liver for me, thanks." so much as it sounds like "No liver for anyone eating at the same table as me."
It's a group game which means that all of us partake of all dishes. Nobody can "eat liver" in a D&D game without my being forced to eat it, too. If someone plays a dragonborn, I have no option to not eat the dragonborn "liver".