Is it possible for stories to hurt you with the audience to backfire? Absolutely, of course it's possible. Stories are not a panacea. If you pick a horrible story that your audience doesn't like, or they're offended by, or it doesn't resonate, it's not gonna help you at all. It can, in fact, damage your reputation. If you're speaking to an international audience of people outside North America, and you want to use stories that all relate to American football, they're going to be looking at you like you're strange and weird because you are strange and weird to them.
They have no idea what you're talking about. If you're telling a story about something that is offensive to someone's religious, ethnic, philosophical belief system, they're not going to focus on your message, or later parts of your story. They're just going to find Do an offensive human being. So of course it's possible for stories to backfire and to hurt you. But that doesn't mean the problem is with stories. That means you didn't select the right stories.
And you didn't test them in advance with the right sorts of audiences.