Nazis weren’t right wing.
Many Nazis were in fact die-hard socialists, who started out as Communists. Goebbels was probably the biggest socialist in Hitler’s inner circle. Hitler was more pragmatic and understood that if the socialists gained too much power in the Nazi movement, they would scare off the German industrialists, whom Hitler desperately needed to help rebuild the German war machine. One of the reasons for the “Night of the Long Knives”, was that the SA leadership was extremely socialist and wanted a complete government takeover of German industry and stipping the industrialists of their control. Hitler did not see it that way, and thus, had them eradicated.