Age is a big factor, grips to young can cause damage to the growth plates in the wrist which can lead to wrist pain later on and even early arthiritis. Grips are safer for teenagers froim about 12 and up. Younger than this a junior grips are preferable. For the very young ones (6 and 7's) is preferable not to use grips yet.
It's very intereting to hear about all of the different rules for gyms. My dd wants grips so bad but our gym wants them to get their hands hard enough to deal with rips.