Karate has more misconceptions and stereotypes taken to the extreme level of stupidity. Kung fu has only a few, such as the Shaolin being super-powered beings who can not only do the amazing things they train for their whole lives, but also fly and control the elements. As for karate, we have "karate is all about breaking wood with the karate chop" (as mentioned in the original post), "in karate you learn how to do the awesome or even gravity-defying kicks from video games, movies and cartoons" (again, mentioned in the original post), "In karate you learn how to throw fireballs", "karate black belts must register their fists as deadly weapons", "karate can teach you how to kill your opponent in one strike" or "if it doesn't require you to wear a kimono (apparently that's how most karatekas refer to their gis), then it's not a martial art". And these are just the ones that came into my mind right now.
Just to be clear, are you saying that you have heard these "karate misconceptions" from actual practitioners of karate? I've met a lot of karateka over the years and I've never encountered one who claimed to be able to throw fireballs or any of the rest of it for that matter. A few of those are stereotypes that people with no experience have about martial arts in general. Some of the others are cliches from cartoons. None of them has anything to do with what karate practitioners do or believe.