Whether or not you have the "right" to be rude, I think the more cordial we are the more we can align around learning through discussion.
If someone is rude to someone who's mistaken that could help them unlearn something, but more likely they will become more entrenched because of consistency principle.
Cialdini talks a lot about consistency principle in his book the "Influence: The Psychology of Persuasion"
I think being rude to someone who's rude to you is childlike and petty. It's how wars start. It's much more productive to either ignore it or try to figure out what's really going on.
It's not always natural and of course we all fail at it from time to time, but justifying poor behaviour because someone else started it just isn't cool.
