The only real way to convince parents that meepcraft is safe for their kids is to have them start playing. Not for just a few minutes as well, but for extended periods of time. Otherwise, most parents know of the Internet as a place where everyone is out to rape your kids and they'll find you just through social interaction. Let's face it, most parents will be skeptical and cautious, but that's a natural reaction for someone who's sole mission is to keep their kids safe from real threats and dangers. In the end, some parents will try and keep their kids off of meepcraft, others won't.
Pro tip: I think either f1 or f2 disables chat until you press it again. It also disables your hot bar and your aiming reticle but it's enough to fool most parents ;)