What is the most libertarian aspect of busybodying children's sports
It would depend if the sports organization was funded via force / taxation or if the sports organization was private.
If it was private, the libertarian aspect would be to support it, if a given libertarian valued it and not to support it if a different libertarian didn't find value in it. It would involve free choice of the individual libertarian to associate or not.
If it were force funded like in a government school situation the libertarian aspect (perspective) would be to malign the coercion. Since to be an actual libertarian you would frown on the initiation of aggression used to fund government schools.
You're welcome, nincompoop.