Perhaps the obvious answer is to deprofessionalise it and relocalise it. Have teams made up of people who live and work near the stadium and fans that know the players.
Whilst this is unlikely to happen another possibility is to have hybrid teams in particular competitions where the hybrid is the best possible team of several teams that are drawn out of the hat. For example, imagine there are teams named A through I. In the normal season all of these teams playing in a league. In the hybrid season, team ABC may play DEF etc. And the next random season, BGI may play CDF etc. As people will always be cheering on people from other teams, the opportunity to create grudges and bigotry is reduced.