I've been to a Caps–Flyers game at the FU Center with the Caps Road Crew, who chartered buses and arranged tickets in a suite. Also been to a UVA–Temple football game at Lincoln Financial Field; for that one we made a weekend trip of it and went to Atlantic City the next day, so we left the car at the hotel and took the subway.
Based on my experience on the Caps trip, and based on my experiences with Philadelphia fans who come down here, if I were to go up there for a Nationals game (which I doubt I will) I'd either take Amtrak and the subway or else park somewhere in the city center and take the subway to the game. The walk isn't bad, it's similar to going from Stadium-Armory to RFK or perhaps a bit shorter. I'm not willing to risk exposing my car to those people. Going to a game is one thing and I can stand up for myself as needed, but leaving the car outside without protection is a risk I won't take, even though there's nothing on it identifying it as a Nationals fan's car aside from Virginia license plates.