As I've done with several of my other communism-related posts in this sub I'll state right here that as a communist myself there is 100% the chance for conflict of interest/soapboxing, and if a moderator finds my answer to contain such, I understand if it is removed.
So first and foremost it's important to have a working definition of what "communism" in the context of historically-existing socialist states means. A simple google search or two will tell you that the official state ideology of every single one of these states (the USSR, the Warsaw Pact, Cuba, China, Vietnam, North Korea, and various others) was known as Marxism-Leninism, but there is both context to be given as well as further nuance to be used here.
Marxism-Leninism as an ideology was formulated in the early days of the Soviet Union, mainly by Joseph Stalin, in the wake of Lenin's death. It considered itself the universalization, refinement, and solidification of Leninism, i.e. the Party's line during the revolution - Leninism itself being the first proper attempt at the implementation of Marxism in its revolutionary form. (Trotsky also claimed to be the 'true heir' to Lenin, so you could say ML and Trotskyism both 'branch' from Leninism, though personally I've seen most refer to Leninism and ML as the same thing.) An important note here is that at no point has 'Stalinism' been anything other than a descriptor of the policies of socialist states, as in, no Communist Party has ever described themselves as 'Stalinist', but as Marxist-Leninist; Stalin is considered not to have changed that much from what Lenin was already doing, or planning on doing.
Marxism-Leninism, as you could probably have guessed from history, drew from the more 'authoritarian' brand of Marxism, which stressed the importance of the state as a tool of dominance in class struggle and therefore considered it immensely important for the proletariat to utilize state power to its fullest possible extent to repress its enemies and promote its class interests. I've elaborated on the nature of 'authoritarian' Marxism several times in the past so a lot of the info you're looking for could probably be found there.
Essentially, though, there was a strong tradition of authoritarian sentiment from both Marx and Engels which is often watered down when discussing their ideology. In the final issue of the Neue Rheinische Zeitung from May 1849, Marx wrote:
We have no compassion and we ask no compassion from you. When our turn comes, we shall not make excuses for the terror.
'The terror', in this case, being a reference to the reign of terror during the French Revolution, Marx implying a proletarian revolution would do so unapologetically to its enemies.
We ought to also keep in mind though, that there were ideological conflicts within Marxism-Leninism, and still are to this day. As mentioned, Marxism-Leninism [came from/is the expansion, consolidation, or refinement of] Leninism, which in turn came from Marxism. Up until roughly 1960, this was what all major Communist Parties believed and adhered to. However, a rift opened between the two major socialist states - the Soviet Union and China - in the wake of Stalin's death, with Khrushchev denouncing Stalin in the secret speech and calling for a policy of destalinization, and Mao in turn denouncing Khrushchev as a phony communist and a revisionist - a capitalist inside the party, consciously or subconsciously leading the true revolutionary path astray. This doesn't exactly bode well for keeping the socialist camp together, and this is what resulted in the Sino-Soviet Split. However, both Khrushchev and Mao claimed to be upholding and continuing Marxism-Leninism. Another wrench was thrown into the mix when Enver Hoxha, leader of Albania and initial supporter of Mao in this split, later split with Mao and took Albania down a third path, which also claimed to be upholding true Marxism-Leninism.
Mao's ideological trend would come to be known first as [Marxism-Leninism-]Mao Zedong Thought (or MZT), then being formulated into [Marxism-Leninism-]Maoism (or MLM) by Chairman Gonzalo of Shining Path in Peru toward the end of the Cold War. The difference between the two is that MZT merely claimed to be an application of Marxism-Leninism to Chinese conditions, while proponents of MLM believe it is a third and higher stage of Marxism altogether, making older forms of Marxism outdated and therefore revisionist (using the same definition I gave earlier). Hoxha's ideological trend, meanwhile, would come to be known as Anti-Revisionism, but is often referred to as Hoxhaism, despite Hoxha not claiming to be of a higher level of Marxism. The trend of the Soviet Union throughout the Cold War would claim to be Marxist-Leninist, but in practice many called it revisionist, Khrushchevite, or Brezhnevite.
It might sound convoluted and confusing, but it was serious business for these socialist states throughout the Cold War - enough for China to invade the Soviet ally of Vietnam and align with the United States in opposing Soviet interventions and support for revolutionary movements across the world. The ripples of this are still felt today - China, which claims Marxism-Leninism as its guiding ideology, actively aids the Indian and Filipino governments against the Naxalbari and New People's Army, who are Marxist-Leninist-Maoist revolutionaries, to this day, though that's inside the 20-year-rule.
So in any case, that's the context of Marxism-Leninism; on to your questions as to what it supports. I'll be answering from the perspective of the Soviet Union mostly, as that's what I know the most about.
Christianity
In theory, Marxism-Leninism has nothing against any faith, Christianity or otherwise. When Marx wrote the famous words "religion is the opiate of the masses", he meant it in the 19th century context of opiates being taken as a painkiller. It was a means of alleviating the suffering of impoverished life under capitalism, toiling for the prospect of reward and the comfort of being appreciated by your God for your sacrifices and devotion, so there would be no reason to repress someone simply for having faith. At the same time, though, given the Marxist adherence to materialist dialectics, religious faith would have no place in policy-making or other theoretical exercise; simply put, the government would necessarily be atheist, but not care about what you personally believed.
In terms of history, though, the Soviet Union was at times repressive of Orthodox Christianity among other denominations. The reason for this, at least for the Orthodox community, was because at the time of the revolution, the Orthodox Church was intertwined heavily with the Tsarist government and the aristocratic landowning classes, and therefore would use its institutional power, wealth, and influence to agitate against the socialist order in the hope of toppling it and reinstating the monarchy. For this reason, Orthodoxy was repressed to varying degrees across the whole of the Soviet Union's existence.