There is a moral panic going on these days about schools performing sex changes on children, or about parents that wanted a girl making their son transition to a daughter and vice versa. Of course, this is not happening, but this scenario have interesting implications.
Let's suppose that schools and parents were changing a child sex for a reason that is not an intense distress expressed by the child about their expressed gender. That would be wrong according to most people. After all, if trans people experience intense distress from being born with their biological sex, we could cause the same distress to cisgender people by making them the other sex. The case of David Reimer, a Canadian man who was raised as and transitionned to a girl after a botched circumcision, exemplify this perfectly. He ended up commiting suicide.
Behind the opposition to this hypothetical scenario comes the idea that children must be protected from the decisions of other people, even if they are related. After all, children cannot make their own decisions, and therefore, society must make the right decisions for them. In that sense, transing a child who is cisgender is wrong because it is a decision leading to bad outcomes. Children are also not the property of their parents.
The state lets parents take decisions concerning their child that leads to very bad outcomes. Parents can decide not to vaccinate their children based on religious grounds, needlessly exposing them to preventable diseases. They can choose to deny them a complete, fact based education by homeschooling them and cherry picking what aspects of the curiculum they want their children to hear about. I have not done scientific research but my experience with people who agree with the second scenario being allowed do not agree about the first one.
People who support parental rights do not actually support parental rights, they want to use parental rights as a way to push their worldview onto their children. They are doing exactly what they accuse the school and the state of doing.
We as a society, should stick to the principle of making the best decision for a child even if it goes against so called parental rights because as it turns out, no one really believe in these, no one really believe your children are your property. If they did, they would have no opposition to a parent transitionning their child to the other sex because they wanted a girl instead of a boy.