Sugar Alcohols destroy me, but xylitol gum, or sorbitol, has never been a problem. I think the amount is tiny and I don't eat the gum. I chew it a lot, normally Trident.
This is my experience as well. Sugar alcohols make me feel horrible (cramps, nausea, bloating, debilitating fatigue, etc.) but I only get that effect from sugar-free gum specifically if I'm ripping through several pieces in a day. One stick of gum isn't enough to do it.