My stance is that it is very complicated, and that there might be no where you can cut that won't be 'to the quick'. Another of my stances is that this doesn't change, regardless of what side of the culture war horseshoe you happen to fall on.
Just because a topic is complicated and you see a lot of lowest common denominator type people take an extreme and simplistic stance on the matter doesn't mean you get to just say what you just said and call it a day. If you don't expound on an actual take that you think is the most reasonable middle ground from your point of view, you're no different from someone who doesn't even care about the subject matter.
From an ontological ethical perspective, it's not even a complicated topic
A child is a volitional being in development, psychologically immature and not yet able to fully express their own will or act on it. Guardianship is the exclusive authority to preserve the child until they can direct their own life. It is a rivalrous right, but this is neither
ownership of the child or its body, nor is it a license to mold them according to some preference
That right is homesteaded by the first to actually perform the work of guardianship, typically the mother from conception onward due to continuous proximity. The guardian's sole mandate is to maintain the child's original, unconsented bodily and mental state (the condition before they are able to agree to any change) until the child can make informed decisions. Interventions are justified only to preserve or restore that state (e.g. life-saving surgery), not to make alterations for aesthetic or speculative reasons
"Best interest" cannot be defined by a court, a culture, or a political faction. It boils down to a single standard, namely actions that prevent conflict between the child's future will and what is done to them before they can speak it. "Parental rights" exist only insofar as they serve that goal. The moment a guardian actively harms the child or obstructs others from taking over preservation, they forfeit that role.
If you see it this clearly, there is no irresolvable clash between "parental rights" and "child's best interest". They are not opposing claims, but two descriptions of the same underlying structure (the right to guard, bounded by the duty not to damage what one is guarding)