I suppose I agree with your sentiment, Gimwinkle.
For example, I may disagree profoundly with the method (or lack thereof) someone is using to raise their child, but that doesn't mean I, or the state, have the right to step in (unless it is outright abusive). That would be authoritarianism. So long as they are healthy, happy and free from harm, there is really nothing we should do about it, except try to appeal to them with reason, which is likely futile.
However, if someone is causing sustained, explicit or long-lasting harm to their child, I think it is the role of society to do something to stop it. I would consider allowing a child to eat unhealthily all day everyday, sustained harm. But I wouldn't call the cutting of the umbilical cord violence, nor the removal of an infected appendix. I would, however, call the mutilation of the prepubescent vagina a cruel and substantial attack on the child - perhaps the worst kind of abuse imaginable, seeing as it serves no purpose except a dogmatic adherence to a cruel tradition.
I also think it's helpful to separate nature from humanity. We have no business intervening in it except to learn important things and to enlighten ourselves. Human nature, however, is its own complex realm of nature, of which we are all a part of, and we are all accountable for the injustices of our neighbours. We can't save the seal without harming the whale, so it should be left as it is. We can make life better for all of humanity, however, by utilising man's ability to reason. Animals can't reason, I think that's an important difference.
It really is a grey area, and I think we should be aiming for some sort of middle ground between parental freedom and child freedom, parental rights and children's rights. But defining that middle ground is probably the hardest part.