If it's any comfort, I've always been one of those people!
I once cried at a parade. A parade! I usually cry when a national anthem or some other ceremonial song is sung/played. I cried while writing the acknowledgments to my MA thesis. And I sometimes get a little teary when an ambulance or fire truck goes past. On top of the more usual things, births, weddings, funerals, sad stories, happy stories, etc.