My older sister was born with a pretty significant birthmark - on her face. It's called a port wine stain and covers half of her face and then some and sneaks down onto her neck as well.
Growing up I don't ever remember it being an issue. I was told many years later that my parents took her to a doctor or two and, as the story goes, (I'm pretty sure I'm not making this up) one of the docs asked her what she wanted to do. She said to just leave it alone. And there ya go - that's how my sister grew up with a red mark on her face.
I also remember (or think I do) that my younger sister and I told the kids in the neighborhood that our sister was half Indian and if they wanted to see her, they'd have to pay us a nickle. Nice, eh?
The other memory I have (I think it's mine, anyway) is that when Max Factor came out with something called "Erase", Stacey gave it a try. It came in lipstick form and was the color of your skin (if you were Caucasian of course) and Stace applied it for the first time just before her friends came to pick her up to go out. When she jumped in the car they looked at her and said, "What did you do to your face?" She told them about this new coolio stuff that covered her birthmark. They promptly told her to go back in the house and wash that shit off her face. Well, maybe they didn't say "shit" but you get the picture.
They were so used to her "real" face that the fake one gave them the creeps.
I don't ever remember her talking about being picked on or bullied in school. Oh, I forgot to mention that she's short too. Never quite reached 5 feet. So being the shrimp with a birthmark may have turned some kids into a shrinking violet but not my sister, Stacey. She's a feisty one and I'm sure that's why no one had the guts to pick on her.