The development in the early 1800s that best represented the continuation of the ideas expressed in George Washington's Farewell Address is the rise of a foreign policy of non-involvement.
Washington advocated for the United States to avoid permanent alliances and entanglements in European conflicts, emphasizing the importance of maintaining independence and steering clear of foreign rivalries. The non-involvement policy aligns with his vision of ensuring that America would not be drawn into European disputes, thereby protecting its peace and prosperity.