Have my parents gone crazy?

Your parents are right. You may think they photo is funny, but as an outsider looking at it, it does make you look cheap, and my attract the wrong sort of attention to you and your Facebook page. As you have no control over who sees your photos over the internet, you should be aware that there are a whole bunch of crazies out there who might see your photo in a way that you don't. Take it off Facebook.