I think part of the problem is the perception of what is a "State" antebellum versus today.
I also believe that Washington did not have to choose between Virginia and a government with which it was at odds. Oh, wait. He did.
It is just that that government was across the Atlantic, not the Potomac.
Lee had served the Army of the United States honorably.
But when called to turn his back on his native Virginia and side against the land of his birth, he would not.
Only the idea of a "State" as the watered down rubberstamp for an outrageously overreaching Federal Government muddies the water, here.
In Lee's day, the Federal government was a Federal one, not a National Government like it is today. Yes, there is a difference.