How the hell do people handle being graceful in the face of others being confidently, dangerously, stubbornly wrong - particularly when they outrank you?

It's a genuine question. I'm decent at my job but I've met a good number who are way better and also totally diplomatic in the face of the relative idiots (including me) . Is it just the fine art of giving less shits?

Welcome to devRant!
It's a hard thing dealing with stupid. Sometimes I just give up and make what they want so they can see the problems with it, usually only wastes an afternoon.

Aside from this, argue. Hope they have the respect to listen to your opinion, failing that there are 2 other options:
1. Bust ass until you're in charge
2. Find a job where you're more respected

I've managed to get on a project on my own so kinda managed 1.

But this is frustrating as fuck bags.