That "stuff" will become really valuable the second it's stolen and you NEED it.
Just leave anything in your stroller that you wouldn't mind being gone when you get off the ride. Not everyone is so honest at Disney.
This is exactly how we feel. Why put yourself through the hassle of shelling out more money or having to leave the park when a small backpack or diaper bag can be so easily brought on rides? We keep a bag attached to the stroller that holds diapers, wipes, snack, etc, but we also carry a small backpack with extra of those items in case our stroller or bag is taken. We carry the bare minimum with us, so taking a small backpack on rides really isn't that bad.