If the hater is a microwave, it is literally not cool for an ice cube to pretend the hater doesn’t matter. Keeping physical distance is its only option. Yes, it has recently become culturally “cool” to pretend that others’ opinions don’t affect us, but we are social creatures.
We are wired to absorb others’ opinions. Your haters win when their negative opinions hit your ears. The best course of action is to “not listen” because “listening and not caring” isn’t humanly possible.