Pretty much any pro sports rivalry has died with the advent of free agency. There are really only a handful of real rivalries left in the pros, and it's mostly the fans that don't like the other team, not the players on the field.
Rivalries really flourish when players on the field identify with their team. With free agency, it's all about being "professional" and not ruining your corporate value to your team or to others.
I watched a bears/packers game from 1985 the other day. It was VERY clearly a rivalry game back then. Guys were laying wood 10 seconds after the whistle blew. They REALLY did not like one another.