A liquid dispenser has a bay surrounded by a shaped frame that is sized to receive a shaped refill inserted at an acute angle of 75 degrees or less in relation to the dispenser's lateral central axis. This unique arrangement is designed to maintain consistent quality of liquids dispensed by preventing the substitution of product refills having different shapes whose contents are of uncertain quality. Refills may be readily manufactured and at low cost. Mechanical and motorized dispensers with optional proximity detection of a user's hand may be used with the inventive dispenser and refill arrangement. Liquid or foam may be dispensed depending on the design of the dispenser pump.
