I know I don't want my parents to babysit my newborn, but I don't know how to tell them.
Oh no? Why wouldn't you want your parents to help babysit your newborn?
I don't like the way my parents act around my newborn.
It's normal to feel protective of your newborn, so don't feel guilty that you don't want to leave your baby other people. However, unless you think your parents are unable to take care of your baby, you should give them a chance to babysit. That is their grandchild, and I'm sure they love her and want to do everything they can to make sure they're involved in her life.
I don't care if my parents are involved. I just don't want to leave them alone with the baby.
This is a common issue with new parents. Your parents have raised children before, so I'm sure they're quite capable of taking great care of your baby. If you're really worried you can stay with them for a while so you can feel more comfortable about making that decision.