While they are common traits, they are not requirements to be considered part of fascist ideology. While used by more famous fascist governments, they are not necessary to impart the general ideology of fascism through authoritarian control by a dictator.
For example the Spanish Falange was considered a fascist movement. It supported conservative ideas about women and supported rigid gender roles that stipulated that women’s main duties in life were to be loving mothers and submissive wives. There was no economic system defining the fascist movement.