(To be clear, I am not a religious person at all, rather atheist/agnostic, but I am interested in the origin of Christianity as such.)
If I understand it correctly, not only private property is a gift from God. More importantly, it is an individual’s liberty (or life, depending on who you talk to). The non-aggression principle is a major consequence they draw from this. This contradicts the notion of a state as a violent „stationary bandit“, which they see as a necessary but temporary evil.
Generally, I don’t see some minor communal obligations as something bad. I think Switzerland is a good example of how this could be realized (maximum local autonomy held together by a bunch of impersonalized abstract constitutional agreements). As people live more and more tightly next to one another, the situation as in Rural America of the 19th century get more and more unrealistic.