Where there is confidence there is love, where there is love, there is peace

How can we remain at peace even when surroundings are hostile

when we get a registered letter from someone, we sign and accept. And then we are aware of the contents, even if we don't accept its contents. The letter goes back to the sender if we don't sign, thereby the sender's purpose is defeated.
Similarly, don't give ears to abuse. Maintain cool and remain disinterested. Then the foulness goes back to the sender and does not affect at all.
It will rather affect the sender as a resound, reaction and reflections. Instead of harming you, it will only recoil the sender.