My group had a lot of fun subverting this in our last game. My half-orc barbarian was a surly teenager who liked to talk about all of the prejudice he'd experienced at the hands of humans due to his parentage, when in fact his parents had been two half-orcs (PCs from a previous campaign) who had won general public acclaim and risen to found a fledgling kingdom, and raised him in relative luxury and with the goodwill of the local populace.
I may have to steal that. Have a PC with "local hero" or "noble birth" as background that's the son of two half-orc parents. He moved to the big city and doesn't understand the discrimination he never felt in his home town.