A few data points:
People here are generally great. I have a lot of close friends, neighbors, acquaintances, and happy clients who are Aggies. Sure, the students go a little nuts sometimes. And there are message board cranks. But I have never experienced "irrational hatred" in person. I have adopted the Aggies as my distant-second-favorite team. It's not that hard to cheer for the Aggies. If I didn't love an underdog, I wouldn't be a BYU fan either. And I like to see the long-suffering Aggie fans experience whatever sports joy they can.
There is a decent number of BYU alumni and fans in Cache Valley, but many of them lay low. Some are employed at USU, receive funding through USU, or have other political/social reasons for needing to fit in. So I was surprised and pleased to see folks I know, even members of my ward, at the football fireside a few years back.
I have been involved in BYU alumni/J. Reuben Clark Society stuff both here and in the other places I have practiced. It has been a tough sell in Cache Valley. In most places, LDS lawyers are happy to have an organization that brings them together. Here, the association with BYU keeps a significant majority away. I suspect others stay away out of fear of being tainted by association. Too bad.
I wear BYU gear around town, have a BYU Law sticker on my car, etc., etc. The worst I have got is harassment from lower level employees in stores. Most are cool. We exchange barbs, and I can usually get them talking about how their team looks this year. They act human when treated with a little humanity. Very rarely, a college kid has been a little rude. I call them on it with a smile, asking if the owner of the store knows they treat customers like this. No big deal.
My favorite story about being BYU fans in Cache Valley: my oldest daughter was in the Cache Children's Choir shortly after we moved here several years ago. The choir agreed to ride on a float in the Aggie homecoming parade singing the Aggie fight song. When my daughter heard about this, she stood up in front of 100+ kids and declared, "I'm not singing some stupid Aggie song! I'm a cougar!" Part of me was proud. The other part of me put together a family home evening lesson about being kind to people who are different than us, that Aggies are our friends and neighbors, etc., etc.