That only works when there's no scarcity. Then its up to communists/capitalists/anarchists/dictators how to slice the cake

Well, it does not have an economy, so why would it have money?

Also, it doesn't have politics and society in the conventional sense, but men are clearly subordinate to God. Christ is king, this is the way Christians think, so I am not sure this is a correct comparison.

The question of "should Christians strive for a classless society" is a complex one. Egalitarian ideals are very new compared to Christianity, but some Christians now think that in the "fallen world" authority is undesirable as it can be abused. This is not common though.

However, Marxism is an anti-religious ideology. Marxists both believe that religion will disappear after "the base" changes and it will become, ultimately, obsolete, and also have historically persecuted and enacted violence on Christians. So I am not surprised there are not many Marxist Christians.

Ooh baby, do you know what that's worth?

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Well that description suits better anarchism. Also Heaven doesn't exist it was invented by catholic church like many other stuff they made out of nowhere. Christian God wants to make a non-human monarchy (so God and Jesus as king) and remove all human based States. So pretty much not a communist. Of course you can argue is not anarchism either and is just common monarchy, since there is still some form of authoritarianism, even if not human-based, but from my personal perspective if it truly were a perfect reign I wouldn't mind at all