First off, don't get why you have a problem with the missionary. So he isn't a BYU fan. Last time I checked, part of serving an honorable mission did not include being a fan of the local school. Second, in Gainesville, and in general the south, there are two types of Mormons...the transplants and the natives. The transplants will include those who typically grew up in Utah or the west and then moved out east. These are your cougar fans. The natives honestly don't care about BYU football. The SEC is so ingrained in their culture that schools out west are merely a side note.
And as a side note, yes, we have had missionaries state they are huge BYU fans in our meetings and not gator fans, but we really don't care.