An avid fan is someone who is really enthusiastic about a sports team and he (or she) watches that team regularly. I really love to read and so I am an avid reader. The adjective ‘avid’ is used to describe your enthusiasm for any activity which you like to do a lot.
If you are an avid fan of a sports team such as Olympique de Marseille, you root for that team when you watch a match. When you root for something or someone, you support them. When our students take the DCL exam, we root for them!
In the cartoon, the lady doesn’t quite understand the level of avid support the men have for the Broncos because they are rooting for the team in the Bronco uniform no matter who the players are. So, she states that they are rooting for the laundry! Your laundry is your dirty clothes that need to be washed or those clean clothes that have been already washed.