This question has been tossed around the Mountain West more specifically between Utah and BYU fans. The rival between the two schools --The Holy War-- is as intense as any other rivalry across the country. However, the Mountain West is in a different situation then the Big XII, SEC, and the other automatic BCS qualifying leagues.
Growing up in Houston the team I followed was the Texas Longhorns and my older brother went to Texas A&M and obviously followed the Aggies, and every time the Longhorns played he wanted them to lose, no exceptions. The Big XII the does not have to have Texas or Oklahoma represent the league, because the league is respected enough and does not need all the teams go undefeated in the non-conference schedule for respect.
Now, the MWC does need every win in non-conference and bowl season for respect. Just look at last year how the league received national attention by going 6-2 against the Pac-10, Wyoming beat Tennessee, and Utah beat Alabama in the Sugar Bowl. For the good of the league all fans should root for each team to win non-conference games. Now that is different then saying a BYU or Wyoming fan rooting for their rival in Utah or Colorado State to win, but rather hoping they win so the league looks better in the national media.
No need to sit in front of the telveision with the buddies while throwing down food and beverages openly cheering for your rival, but it is reasonable to sit back and hope they win because in the long run these wins can help your own school.
This choosing to root for your rival is big this season with BYU playing Oklahoma, Utah going to Oregon, or UNLV playing Oregon State. Now there are fans who from any rival squad and no matter what want their rival to lose every game, and in my opinion those fans are stubborn and do not see the big picture. Logical fans should want the non-conference record to be 32-0 --even though that is unrealistic-- to show the nation that the MWC is a good league. The Mountain West is starting to prove they belong in the BCS, and so why wouldn't fans want opposing schools in the league to win big games, because in the end the rival may be the team that gets the league over the top.
However, when the rival comes to town, yes heckle and boo the opposing team, but with the Mountain West trying to get to earn an auto-bid to the BCS fans should cheer for the league to win those high profile games.
So, do you cheer for your rival, or want them to lose every game they play? Tell us Why?