Patriarchy,
If you lived in a culture where tattooing babies were normal, I would argue for that right, yes.
Parents can give consent to babies undergoing procedures unless the harm is clearly shown to outweigh the benefit, and the harm is beyond a certain level. This is clearly subjective, which is why it is legislated on.
Equally you are refusing to properly engage.
IS the issue trauma to the baby/adult? Is the issue consent? If the latter, why does medical opinion override consent unless it is critical and urgent?
It seems the issue to most is a melange of things mixed up in their heads with a strong underpinning of subconscious cultural superiority