There are huge differences in socialism and Separatism/Puritan and Quaker theology. Even within Puritan theology, their eschatology changed over a century from when they left England for Holland and when the Quakers began to intrude upon the Puritan Separatist magistrates in New England. In the early 1600s they tended to be Millennial, while towards 1700 they tended towards Post or Amillennial eschatology, making tremendous differences in their theological perspectives.
For several centuries entire villages were slaughtered in Europe if their theologic perspective wasn’t the same as others in power. The State was frequently identified with the Church and theologic differences were identified as not only blasphemous but also treasonous and criminal.
They were hardly cults. They came to the Americas because they rejected the ritualism of Catholicism and the Church of England, and because Calvinism and the Reformers were also closely associating the Church with the State.
Jim Jones was much closer to atheistic in his perspective, seeking a cult power play amongst his followers and bouncing between numerous liberal theologies, but never following the fundamentals of Christianity.
Regarding the association of the Pilgrims with Socialism, the more accurate association is with their common shared resources when inadequate resources were available to keep alive in the physical elements without close community bonding.
As soon as they were able to support separate bldgs and family structures, they drifted away from common bundling of resources and favored independent living, with common Church and parallel Government.