In other words, it's not that being a ute fan makes you drink, but drinking may make you a Ute fan.
I'm active LDS, but try to put yourself in the shoes of a Non Mormon or inactive Mormon living in Utah. There is some stigma and judging that goes with drinking and living in Utah, though it is getting less. Maybe you went to High School and wanted to date an LDS girl and she said she only dated Mormons. Or maybe you enjoy a beer and dislike the regulations that make it tough to get beer with a reasonable alcohol content. Or perhaps you are inactive and your grandparents were disappointed that you didn't serve a mission while your cousins did, (this is the case with my cousins who were in the military instead, but are still considered disappointments in the eyes of my BYU-loving grandparents). If you want to pick a local team, Utah is really the only choice, even if you didn't attend the university. Why would you be a BYU fan when you feel singled out or judged by the LDS church?