It has nothing to do with tznius, and everything to do with looking unattractive. People should take a video of their loved ones chewing gum, and show it back to them. They may not realize how they look.
But as someone pointed out correctly, they might be on a diet, or have a dry mouth, or any other reason for chewing gum. It is not our business,and we have enough issurim that we want our kids to follow without imposing additional restrictions on them.
BTW, would you feel the same way about rebbeim who chewed tobacco?