Trolls. In any environment, people interested in reactions occasionally wander in. These people should be banned and ignored. Shunning is not a particularly nice thing, but even polite feedback is feedback. Do not feed these.

Agreed - but the process of determining trollhood should probably be nice.

The ineducable. Suppose a person asserts that the Monty Hall problem results in a 50-50 chance of switching or not switching. One or two efforts to educate nicely is good. Additional efforts are wasted and unproductive.

There are nice ways to give up on teaching people. Some of these go by names that sound horrendous to our collective project here ("agreeing to disagree"); some may be more palatable ("changing the subject"). Only if the person is hotly intent on mis-educating you (or others whom you feel are themselves educable) does this quality warrant discarding niceness, and it's probably just a special case of trolling anyway.