Christianity, and all other religions for that matter, are NOT anti-communist or anti-capitalist. Most religions were thought up a long time before the concepts of capitalism and communism existed, so how could they possibly be?However, religion does have a built-in defense for the modern capitalist system. It dopes. The promise of 'a better life beyond', an 'eternal friend and saviour in God/Jesus' and a look-up user's manual to Living (with its own complete set of rules of course). When we have all that, and the idea that our good actions are those God acts through us, there's not much need to think independently. It allows us to live in happiness because of the knowledge that when we don't question the Bible and recognize that the highest law is God's word, we are told that something much better awaits us, so we needen't really care that our current life is not necessarily so good at all.
Interestingly, religion was enough for feudalist and despotic systems to keep people in check, but today the capital has much a more sophisticated arsenal at its disposal. Religion tells us that happiness is to follow the Ten Commandments and most of the time let God do the thinking for us. Mass media tells us that the highest possible virtue is to look good and either be a doctor, a wealthy lawyer or an all-american hero blasting communists. Advertising tells us that happiness is a Big Mac Super Menu or a brand new hair-care lotion.
But communism shouldn't actively fight religion. That would very much end up as it did in Soviet Russia, where they abolished the church and built a Lenin mausoleum, replaced Jesus with Lenin and the disciples with Stalin. No, if we wish a society that doesn't need to drug its citizens with religion and mass media we must make society better, then with the negation of capitalism the negation of its drugging influence will inevitably follow as soon a type of person exists who realizes that he does not need the modern Trinity of God, Rambo and McDonalds. A type of person that craves to be sovereign of his own life and not let any of those three rule it.
"They keep you doped with religion and sex and TV
and you think you're so clever and classless and free
but you're still fuckin' peasants as far as I see
and a working class hero is something to be"
-John Lennon, "A Working Class Hero"