Preventing flow of undesired fluid through a variable flow resistance system in a well

A flow control system for use with a subterranean well can include a flow chamber through which a fluid composition flows, and a closure device which is biased toward a closed position in which the closure device prevents flow through the flow chamber. The closure device can be displaced to the closed position in response to an increase in a ratio of undesired fluid to desired fluid in the fluid composition. A structure can prevent the closure device from being displaced to the closed position. The fluid composition can flow through the structure to an outlet of the flow chamber.