Who decides if you are white?

Just a comment, I am a "white" women (gentically just a mutt I guess) who grew up in a bi-racial family. Maybe because of that background I am confused. Who decides if you are white? I have met racist before in my life and none of them would have thought being white include people from Iraq or Isreal There are very few people that are trully white but it seems odd to me to see someone who is "of color" consider themsleves white yet discriminate against other people of color.