Handling haters is more about being able to develop conflict resolution skills. You’ll have people that are constructive or deconstructive with their criticism but they key is to remain reasonable and stick to the facts. I like to come to conclusions slowly and hold on to them loosely as more or better information comes in.
Haters will either be misinterpreting or using misinformation when they draw conclusions. If they interpreted things more objectively and had all the facts from both sides, then they would be an informed discussion partner and not a hater anymore.
You can’t control what comes out of a haters mouth (in person) or fingertips (online). All you can do is understand how to handle them better and many times it involves providing one reasonable response then seeing if they can be reasonable too. If not, distance or delete them from your life or comments section.