Probably not very long. There was already a man in South America who identified as female in order to take advantage of females in his country being able to retire earlier than males, a male in Canada identifying as female in order to get cheaper car insurance, and a male in Canada who identified as female in order to get sent to a female prison instead of male prison.

It's probably going to be a problem as long as "you are whatever you choose to identify as" and "people that identify as certain things deserve govt regulated special treatment" co-exist as concepts.