How is abolishing the family a copy of Christianity? Same goes with private property.
Its not a copy, as such, but as in Satanism, a corruption, a sort-of twisted image.
Note that, for instance, Chernyshevsky (great influence on Lenin) required that the proper revolutionary be like a monk (the model being Orthodox monks), dedicated to the revolution at cost of all family, all self interest.
A very great deal of communist writing, Lenins for instance, is chock full of religious concepts and analogies.