live there (one of which is a very decent sized donor to ASU of over $1 million annually), there is a mixture of things. First, there is an underlying dislike of the LDS in many ways as there are so many of them in the valley, it inevitably collides with the school just by sheer proximity.
Second, the LDS ASU kids I have known are usually more BYU haters than even the LDS yewt fans. My cousin's son told me he watches every BYU game just to cheer against them. He would sometimes not watch ASU games when they were bad, but would never miss a chance to watch and cheer against BYU. His father (the >$1 million donor), and many others that I know applied but did not get into BYU. Another one of my family members that is anti BYU went to BYU, but then did not make it into their dance program. She transferred to ASU and was accepted into their dance program.
Whether or not they applied to BYU, those that go to ASU have hate BYU because they think they are elitist. I have heard from literally dozens that they hate BYU because all the kids from their home wards that went to BYU acted morally and mentally superior to them. I met many kids that told me that seeing this growing up was enough for them to not even apply to BYU.
So, TLDR, the non-mormons hate BYU because they do not like our religion and the whole morality we try to portray. This is compounded by the LDS devil fans that also hate BYU because they either were not accepted, or they were turned off by what they believed were BYU people thinking they are better than everyone else. The two types of fans then bond over their hatred of BYU, even though the first fans would openly mock their religion even after the game is played.