As a parent, I'm not as concerned about my rights as I am about my responsibilities. I have a responsibility to make sure my sons are safe, warm, and well fed. I have a responsibility to teach them the rules of our society. I have a responsibility to educate them. I have the responsibility to teach them to get along with others.
Some parents think they have the "right" to spank their children; I believe I have a responsibility to discipline them gently and positively. But they are correct, I guess - in the US, at least, they won't be arrested for spanking their children. Is that what makes a "right"? The fact that something is not illegal?
ETA: When my kids get their drivers licenses, I have the right to limit their access to a vehicle. But this is more of a responsibility - to keep them and others safe.
For anything I can think of as a "parental right", I can come up with a responsibility to match.
I can't think of any way that circumcising a baby is a responsibility.