A wealthy person in Los Angeles, California, who decides to never own a car could be considered as part of a (n)

Counterculture

Explanation:

The counter culture was initiated in America in the old centuries, and it lasted for a decade, and the Americans got involved in the Vietnam War. It was defined with conventional social norms rejection. The youths, however, did not accept the cultural standards of the parents regarding the racial segregation that had initially spread due to support from the Vietnam War

Therefore this can be equated with the person in Los Angeles who would not wish to have a car because of the norms and believes surrounding the society.