I am still involved in the wonderful sport of gymnastics. As judging on this does have an subjective element (although all judges, at all levels, have to attend several days of training courses and sit rigorous exams), there are often complaints by parents, - with little or usually no knowledge of what they are talking about.
Only the gymnast coach may put in any sort of appeal on a score.
Whenever a parent complains to me about their perception of incorrect scoring, I always have a stock reply and tell them that more judges are always required (clubs have to supply these in order to enter competitions), so they should arrange with their club to attend a judging course (minimum three full days), purchase/download the current Code of Points, spend many, many hours studying, watching videos, asking questions, etc. etc. take both practical and theory examinations - and that (assuming they pass) will bring them to be a Club Judge (the lowest end of judging). Without all of that, they should keep quiet.
We also have rules that clubs have responsibility for the behaviour at competitions - not just for competitors and coaches, but also for their supporters. Bad behavior can get the club suspended.
A good parent of a child sportsperson, takes and collects them in good time, pays the fees, and is always supportive of their child when talking to them about how they are doing. But......NEVER tries to coach them, never puts another child down, never talks about it being 'unfair'.