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.
https://es.m.wikipedia.org/wiki/Paseo_(fusilamiento)
surely the purging of the right wing was not that big in numbers, given that most of it was in the other side of the war.
I think you're correct that with the right interpretation of history, either side could be made to look like the authoritarians.