Personally I'd love to make a timeline where this happens and its based on geography. The reason for this is that in the early 1900's the Cal-Stanford game was actually a rugby game from 1906-1914 and only changed because Cal didn't agree with Stanford's use of freshman on the team and it was so bad of a split that they didn't play for two years. Anyways, during this time, it wasn't only Cal and Stanford, but USC, Nevada, and Santa Clara who played Rugby as well as other teams. Basically rather than switching back to football, you see teams in California Nevada, Oregon, Washington and Idaho play Rugby instead of football. Eventually the west becomes more of a Rugby while football is popular east of the Rockies and in the Southwest in Arizona and New Mexico.
If such a thing happened, I'm guessing college stays the big game as its amateur, though you do see teams of ex college players form in San Francisco, Oakland, LA, Portland, Seattle, Sacramento, Spokane, San Diego and even a team from Vancouver joins the league which eventually becomes the American Rugby Federation. Eventually this league expands to other cities like Salt Lake City, Las Vegas, and even football areas of Denver and Phoenix. Football however does get some crossover out west, but Rugby remains king on the west coast.
My big question is how would you introduce professionalism. This was a huge debate in England and Rugby Union was always an amateur sport in Britain and other counties as far as I know.