Is Communism a modern doctrine? Or born of the Enlightenment?

Is Communism a modern doctrine? Or born of the Enlightenment?
Heavens, no.
Brief history-of-politics series of points, in response to this question from a few places on social media:

1. For millennia all communisms were religious. (* exception at end)
2. Think of the many religious monasteries and convents, populated by those who see their life’s moral calling to be to serve their God purely and consistently.
3. How does one do that? Their social model was entirely communistic: no private property and no individualism. Everyone eats, prays, works, and sleeps communally—and selflessly serves the commune and God.
4. For many centuries that model was upheld as the highest approximation to an ideal possible to humans on Earth—and that the true ideal can only be realized in the World Beyond.
5. What happens, though, in the early modern world, when the belief in a World Beyond comes to be questioned, then challenged, then doubted?
6. Some modern thinkers will then abandon the religious *metaphysics* of a God and World Beyond—but they will retain its *morality* of egalitarian service and its ideal of communism, along with its hostility to private property and individualism
7. The two clearest examples of this dynamic are Jean-Jacques Rousseau and Karl Marx, the founders of the two most prominent versions of communism in the modern world.
8. Rousseau is “modern” in his abandoning traditional religion for a sort of softer theist-deist religion, though one that will be hardcore enforced by the State, the State vigorously using religion to enforce its egalitarian communism. Different metaphysics, same-old political ideal.
9. Marx also is “modern” in abandoning religion, more ruthlessly than Rousseau does, at the same time calling for a violent dictatorship, after which the lions will lie down with the lambs, i.e., the exploiters with the exploited, and an ideal communist society will emerge. Different metaphysics, same-old political ideal.
10. Thus, communism is an ancient religious ideal, hanging on in the modern world due to the reactionary efforts of those unwilling to modernize their morality.
11. (* Exception: Platonic communalisms, inspired by *The Republic*, written by that most religion-friendly of the major Greek philosophers. There Plato argues that the highest class of people, the Guardians of society as a whole, will renounce individualism and live entirely communistically.)