I think it depends on what kind of workout/activity you have planned for your client. Tell a major league pitcher not to chew gum (or whatever!) and pitch and you’ll be laughed out of the park. I do think that in general the risks of choking outweigh the benefits of chewing gum in a typical fitness workout. You’re the trainer, you’re in charge.
As a general rule I would say no gum chewing during a workout. Just drink plenty of water!