The best example I've seen lately is Richard Dawkins, who posted a video I won't link to where an Islamist and a Feminist are singing a song together. The video makes a real point that isn't intrinsically offensive. But the highly caricatured portrayal of these two people is, to me at least, a pretty inflammatory gesture. Also it came out that the feminist caricature is based on a real person who has received death threats for her work.
Humans aren't programmed to live together with people who are really different from them. We evolved to preserve our in groups and unify against out groups. We have huge blind spots about how other people will perceive things. We can absolutely learn, but it takes effort and we'll make mistakes as we go. Twitter is all of this happening in real time.