I've only Posted on this site a couple times and each time has been a negative experience. Hope that changes.
To get back to the topic of this post.
I feel that it all depends on the relationship between the coach, parents and students. The atmosphere/history of the club.
One TKD grandmaster I trained under encouraged trying different styles.
Aikido grandmaster wouldn't let you practice outside of the gym.
Our head gymnastics team coach is secure enough to know the Parents and kids listen and respect him equivocaly.
Our boys will train with an assistant coach or camp coach, Uncle Buck...but know that he "Coach" has the final say with regards to techniques.
I will caution that injury is more likely to occur when mixing styles.
We had 1 kid break his toe week before Regionals trying to get in extra training.