These differ in intent. The climate activists don't hate the underlying art, they just want to do some kind of stunt that gets people in the news. That's why these protests targeted art that was stored behind plexiglass; they wanted a protest medium that was highly disruptive and shocking but caused minimal harm.

ISIS on the other had specifically wants the art destroyed because their particular brand of brainworms is opposed to anything that isn't worm-shaped. The goal wasn't to shock people, it was to cause deliberate damage to human culture.