Not so much the view of the parent, but of his whole family. Since you're using a family analogy yourself - let's say you have the Fallout clan, a family of hardy men who came to America seeking a better life.
You have Cristopher Fallout, the patriarch, who is really into the progressive rock he listened to in his youth. Then you have his sons Jeb, Clem, Earl, Bobbi Jo, Mary Lou, Trixie, Crystal, Billy Bob and Carl Fallout, who are all hardcore fans of Insane Clown Posse. Do you think they should be known as the Prog family, or the Juggalo family?