If public service is what you want to do, you should do it. There will be shutdowns and bureaucracy, but that is part of the game. Just like professional athletes lose half their season due to labor disputes, keeping them from the game they love, civil servants are often stymied by administrations or legislatures that care more about branding than results.
If it is just a job to you, don’t bother. But if you want to make a difference, by all means join.