I can't chew gum due to my dental work that I had done a few years ago. It sticks to everything and I have a bigger mess. But even still, before then I couldn't chew a lot of gum because I'd wake up in the middle of the night grinding my teeth and in a lot of pain the following morning. I've always been told to not chew gum due to grinding my teeth.
Do I mind others chewing? Unless they are chewing like a cow, rudely popping bubbles or playing with their gum then I don't really care. I mind the chewing sound and have found myself gagging/vomiting from the sounds of it. I find it very rude to have bubbles popping as it's very distracting especially in places like church, school, etc. And playing with the gum...that's just germs. Eww!