I went to grad school at BYU, and I cheer for the Cougars 11/12 games a year.
But I got my Bachelors Degree at Utah, and I'm all in for the Utes.
I want Utah to beat BYU- but I'd happily trade a win over BYU for a win over UW, or USC. I don't really think that losing one game vs. BYU is really going to affect Utah's recruiting effort. But winning the PAC-12, and the Rose Bowl could benefit their recruiting effort a lot.
I personally don't think Utah and BYU go head-to-head on THAT MANY recruits. If you look at the rosters, over half of BYU's players are from Utah and Idaho. Utah's roster is only about 1/3 Utahns. They have more kids just from California, Texas, and Florida combined than they do Utah.