I've long since stopped worrying about the ignorant in the world
I agree, life it too short to worry.
I usually just reply "it's not a skirt, it's a kilt"

Sometimes I ask them if they know why it's called a kilt, they say 'no', "that's what happened to the last person who called it a skirt" (they were 'killt').

ie, I make a joke out of it.