Fascism and socialism do not have anything in common. "Central planning" is not fascism; it can be done by the people. "From each according to their ability, to each according to their need" - a thing no fascist would ever say.
Fascism is capitalism in crisis. Read R. Palme Dutt's scientific investigation into the subject, Fascism and Social Revolution.
Socialism is the lower stage of communism, a proletarian state with a goal of abolishing class. It is significantly further away from actual fascism than you can imagine.
People need to learn what fascism actually is before they call everything they see "fascism" on the internet.