You're too optimistic.
The fascist plan is to sow discord and confusion, chaos. They are in a minority and can function most effectively in an environment where the mainstream is divided and confused. Its how Hitler worked in the 1920s, and the Bolsheviks did it in Moscow in the 1910s. Its how Castro took over in Cuba. In each case, a small cadre of radicals was able to outmaneuver an entrenched bureaucracy of "moderates".
A small and outnumbered but determined and disciplined group can overcome a weak and divided majority only by provoking a melee, the environment where their lack of a solid hierarchy and centralized leadership is an advantage.