Save your own face

As a rule you don’t give haters the light of day. Say for example that hater is talking to a room full of other people, then it’s a different story. In that case, not giving them the light of day can backfire, as you can be seen to be inattentive and disrespectful. There you can give them the light of day, fake if necessary. It takes a bit of biting your upper lip, but anything that could damage your reputation is a plus for them.