“The oddly political aspect was that it mocked the anti-communist fears of the 50s, while thoroughly demonizing the Soviets.”
You are correct. The film ridiculed those crazy rightwingers for fearing the commies, yet portrayed dozens of homicidal commies running around IN THE US, murdering US servicemen by the bushel in a bid to take over the entire world.
Did Indiana say, “Commies...I hate those guys.”