Since Conan: The Adventurer was a cartoon for kids. Instead of The Snake Cult killing Conan's family which would be too strong for a kid's cartoon, it was decided Conan's family gets turned into stone statues.
The Snake Cult in the cartoon is different from The Snake Cult in Conan the Barbarian (1982) which the cartoon is based on. In the film, The Snake Cult is led by the evil sorcerer Thulsa Doom and in the film, Thulsa Doom and his warriors raids Conan's village and slays Conan's tribe including his parents. In the cartoon, The Snake Cult is led by Wrath-Amon an evil wizard and Wrath-Amon turns Conan's family into stone statues.