Washington believed in country over locality and the rule of law. He didn't hesitate to send in troops during the Whiskey Rebellion, I don't see him supporting the Southern rebellion as well. Certainly not for the reasons they revolted.
Washington was a Virginian, just like Lee. The two men are interchangeable. Lee would have done what Washington did in the late 18th century and Washington would have done what Lee did in the mid 19th century.