Republican Spain had quite the Authoritarian cut at the time. The radical left was pretty much willing to purge anyone that was anything to their right, and they were the strongarm of the Republic.
The radical left in Spain (including even the Anarchists who were a significant poltical force at the time) supported the Republican government. The purges that took place on the left, were the purge of the POUM (Trotskyist, the group Orwell fought with) and then the CNT-FAI (anarchist) by the Communist party (Stalin/USSR). Both purged groups were considered to be to the Left of Stalin by all sides in the conflict, the purged groups certainly were definitely less authoritarian.
The incumbents always look more authoritarian than the revolutionaries, who are by definition trying to overthrow some of the institutions that the first guys control.
I think you're correct that with the right interpretation of history, either side could be made to look like the authoritarians.