To up sticks means to relocate from one's current residence, so the context is saying that the only option is to leave and move to a new place.
Consider the staetement "It quickly became apparent to pretty much everyone that the only viable option was to leave and move to a new place.". Based on this statement, is "It quickly became apparent to pretty much everyone that the only viable option was to up sticks." a true statement? Yes/no/unknown