Well, you could have just told them she's a mixed race and is neither black or white.
At 5 years old, she's just going into kindergarten. She's going to find out about race on the playground. You can't shield her from that.
So the school wants to track the race of all students. Why? Statistics. It's not really for evil. And both white and black school administrators want to keep track of student race population, it's not a racist thing. They aren't going to treat her any different. Ultimately, you want to establish a good relationship with the teacher of your daughter's class.
If you barge into the prinicpal's office yelling about the Illuminati, the man trying to keep you down, Tyler Perry movies, and poking your finger through toilet paper unappreciation, they are going to think you are a crazy parent. Putting down mixed race is a small detail. Having to deal with bullying is a way bigger problem.