I feel like we don't even really have a rivalry with Washington anymore. If you're around my age, you'll remember how intense the Dallas/Washington rivalry was in the 70s. Both Tom Landry and Washington Coach George Allen built some great teams. When their two teams met, it was almost always a dog fight. The Rivalry resumed some in the 90s with Coach Johnson versus Coach Gibbs, though maybe not quite as insanely intense, but definitely with some outstanding teams. I remember when it was Washington week, the whole family looked forward to the game all week, and we sometimes had friends over for parties to watch.
Today, if we're playing Washington, it just feels like another NFC East game. It seems like we're just two other competent NFL teams playing one of 17 games. I have way more contempt for the Eagles than for the Commanders. And the Eagles have been way tougher competition in recent history than Washington. So there is a rivalry against the Eagles, but I still don't think it's anything like the Dallas/Washington rivalry of the 70s.
Does that really matter though? Do you need a quality rival to be able to build a championship team? Or could every other NFC East team stink, but we would still build a championship-level team?