The only fuss I recall over Conan was the alleged use of trip wires on the horses, which director John Milius denies ever happened. Lots of horse owners in California, and I saw protesters with signs at one theater local to me back in '82.
Beastmaster came out three months after Conan, so I don’t see how it’s considered a knockoff anymore than The Sword and The Sorcerer which opened a month before Conan. And you had Thundarr The Barbarian on Saturday mornings two years before Conan even came out.
Remember when all those underwater movies came out around the same time as The Abyss? It just happens for some reason. Beefy guys with swords were suddenly in vogue in the early '80’s.