I believe there are some hand sanitizers (probably more common for commercial uses) out there that use quaternary ammonium compounds. Those are corrosive but shouldn't really cause problems with stainless steel. They will turn brass green and, I suppose, could be an issue for blued finishes.
Benzalkonium chloride is a common anti-bacterial ingredient in hand wipes and similar products. As far as I can tell, at the concentrations they are used in those products, they shouldn't be an issue.
Alcohol (ethanol) is common in the gel-type and some liquid type hand-sanitizers. It shouldn't be corrosive, but the alcohol could potentially damage anything that is sensitive to solvents. I wouldn't expect it to be an issue for plastics or metals, but it could be an issue for some wood finishes.
Finally, nearly any product that's designed for skin is going to have at least some water in it. We all know about water and its effect on metals.