“If someone is being an asshole, is it wrong to stoop to their level?”

If you’re past high-school age it’s time to realize that even though the answer might be no, you’re asking the wrong question.

The question you should be asking yourself is “Is there any fucking point to engage with people like that whatsoever?”
And the answer to that is a no.

You can get down in the mud and wrestle with the pigs if that’s what you want, and you can make yourself feel better by telling yourself they started it, but in the end nothing good will ever come of it. You just get muddy and tired.