Don't ruffle my feathers.

The phrase to ruffle your tail feathers means to annoy someone and get the angry, when a ducks becomes frighted or is bothered it makes itself seem bigger by ruffling its feathers so it puffs up.

Please dont ruffle my pet doves feathers!

It is interesting to watch a wild turkey ruffle it's feathers.

If you bother a bird, it will ruffle up its feathers in irritation. "Don't ruffle any feathers" is just an idiomatic way of saying "don't annoy anyone" or "don't stir up any trouble."