I have a hard time seeing BYU replaced as the Utes' main rival. CU is in a differrent situation though. They never really had a conference rivel until Coach McCartney designated Nebraska as their rival back in the 1980s. Nebraska though never considered CU to be their rival...even after the Big 12 was later formed. Thus, it was a one way rivalry. Nebraska fans did build up a healthy contempt for CU fans, who they considered to be the most boorish in the Big 8 then Big 12.
Now CU has to go a lookin for a new rival. Utah might become the designeated rival. Who knows? BUt I cannot see it becoming as heated to Utes as the BYU rivalry.
As a parralel. When Florida State joined the ACC in 1992 folks wondered who their rival was going to be? At the time, most thought that it would be Clemson. However, that never materialized. Florida remains as FSU's main rival. Within the ACC, they never developed a true rival. The same may hold true for the U and for CU in the PAC-12.