I agree with Val that some aspects of the parent posts sound a bit adversarial. The most contentious point may be that the activity needs this particular child in order to be competitive and therefore it would be "stupid of them" to expel a child for back-talk and poor behavior. Some may say that there are more important experiences for seven-year-olds than winning, such as demonstrating teamwork and respect.

If an adult tends to see a particular child's activity first and react to that child first, it may be that the child is a leader or instigator who can quickly get others off-topic and/or disregarding the rules.

I'm sure the situation can be worked out for the benefit of all involved.