Before Pearl Harbour got the USA into the war Stalin was prompted by Roosevelt to change the Soviet stance against religion “as a means of tempting the American public to give its all-out support.” Indeed the press in America had a major problem about Russia being so dreadfully irreligious - vis New York Harold Tribune in October 1941:

If the Soviet government were to yield … it has to disband the Atheist League. … It would have to allow the Russian Church to call a Council for the election of a Patriarch. It would have to give permission to reopen religious academies, seminaries, and schools. It would have to return to worshippers at least some of the churches, long ago converted into dance halls and museums. It must give assurance to the population that their church attendance will not handicap their state jobs. … To grant all these reforms, the very idea of Communism will be defeated.

The Soviets followed heed by

• closing down the Atheist press

• reintroducing the old church hierarchy. Sergius of Moscow, who has been part of the high clergy since before the revolution, would enter exchange with foreign church leaders in 1941 and would become the first patriarch since 1925 (when Tikhon died) in 1943.

• introducing chaplains for Polish units

• printing pro-christian articles in the press

• for the first time for years Easter was celebrated in all Moscow churches in 1942

• Soviet dignitaries would attend the services in the British and the Polish military

The British would support their efforts by, for instance, appointing William Temple as the archbishop of Canterbury in St.George's Day 1942. William Temple was an anti-fascist clergyman and previously wrote books which worded out a very clear preference for Marxists over the still formally religious fascists (which was a very unusual opinion for clergypeople at that time); under his lead the Anglicans would distribute literature aimed at increasing trust towards the Russians in the foreign Christian clergy (attacking mainly the Nazi narrative of a holy crusade).

Reactions were very different and ranging from full enthusiastic support (along with an request to sell them as many copies of the book as possible) by the exiled Armenian Apostolic church to a clear rebuke by the Russian Orthodox Church Outside of Russia (whose first hierarch Anastasiy already was on pronouncedly good terms with Adolf Hitler.)

Source: The Russian Orthodox Church 1917-1948 by Daniela Kalkanjieva

The Russian Orthodox Church would stay loyal to the Soviet leadership; ROCOR naturally relocated wholly to the United States and got involved in various propaganda efforts like Radio Liberty. Soviet attitudes towards the church fluctued strongly after the war but the pre-war era anti-clericalism had never returned. In 1939 there were only a few hundred working church in Russia. By 1945 there were 10,044 and the number kept increasing up to 14,477 in 1949. Of course the church was not officially endorsed and church involvement looked bad on your CV.

In 1987 loosened censorship lead to an explosion of Christian themes in cinema, music which left a dent in the attitudes of the protest generation middle class.

source: Religion, State and Politics in the Soviet Union and the Successor States, 1953-1993

What's not covered by the scope of /r/askhistorians:

In 2007 the schizm between the Russian Orthodox Church and the Russian Orthodox Church Outside of Russia was finally mended. It didn't happen earlier because the ROC spend half the previous century attacking ROCOR as nazi-collaborationists-turned-spies-of-the-CIA and the ROCOR mostly returned the favours by attacking the ROC as atheist shills on the paycheck of the KGB. However there remain some splinter churches like the more liberal OCA (which split from the ROCOR back in the 1970s).

The attitudes in the other communist countries depended on their attitude towards the soviet and local issues. In East Germany and the Czech Republic the communists already had a tradition of cooperating with the Christian left and would tolerate christian institutions organizing their own events. They would also make cinema about such christian leaders as Jan Hus and Thomas Müntzer which all prevented the religious renaissance that happened in Russia in the end of the 80s: The Czechs and the East Germans are, for the most part, atheists today. Albania is another interesting exception which went into the other extreme. It was not liberated by the Soviet troops but by communist partisans after WW2 and remained opposed to the Soviet Union. They regarded the relaxed post-war Soviet attitudes to religion as a treason of the tenets of historical materialism and would be even more militant in their atheism than lenin-era bolsheviks. For instance, all "religious" personal names have been banned and place-names with religious connotations got removed. "Religious propaganda and the production, distribution, or storage of religious literature" was penalised with 3 to 10 years of prison. For Albania the point was not just ideological competition in the communist block. Like Yugoslavia the country had sizable Muslim, Orthodox and Catholic communities and strict secularism was ought to mend this schism.

I can only speak for Second Yugoslavia, not for other countries.

In general there were three broad phases how state dealt with Religion. My posts will be speaking about Orthodoxy and Catholicism, I am not well versed on others.

Phase 1. (1945.-1950.)

State used large number of violent methods to supress religion. Justification was that they were actively participating in puppet regimes. Most of these charges were trumped and later proven false. Large number of priests and lay people were either shot or imprisoned. People were discouraged from actively participating in religious ceremonies. Top leaders of Churches were physically assaulted or kept in prisons under false charges for long time. Cardinal Archbishop of Zagreb Alojzije Stepinac until his death in 1960. was kept first in prison then in strict house arrest. Metropolitan (Orthodox bishop) Damaskin of Zagreb was beaten in 1947. Metropolitan of Skopje Josif was driven from his parish then was imprisoned in 1950. Overall goal was to remove any kind of Church influence from Society and reduce it to something private. Many acts of violence were random though most of them were centrally planned. For example letter by Orthodox bishop Joakinij in 1945. said that 46 Orthodox priests were killed in Montenegro. Letter of Croatians bishops adressed to Tito in 1945. reported that 243 members of catholic clergy were killed, 169 imprisoned, and 89 missing.

Phase 2. (1950.-1970.)

State did not practice open violence anymore. But religious sentiment was still supressed. For example state decreed that only one seminary (Catholic college for priests) was allowed. Priests still could be randomly detained if state did not like what they said. Churches could be built or repaired only under explicit order by Federal authorities, which was very rare. There was widespread book and movie censorship. State openly promoted atheism and deemed religion as something outdated. You could not advance in political or military ranks if you were religious. Authorities openly meddled in religious congregations. For example they tried to seperate Catholic Church in Croatia from Vatican by encouraging dissenting priests to join state sponsored organizations with ultimate goal of creation state run Church.

Phase 3. (1970.-1992.)

Religion was now somewhat tolerated. State allowed creation of some religious lay organizations. Some of previous bans were either removed or eased. Still open religious sentiment was frowned upon. Best way to practice religion according to state was in your home. But you still could not advance in political or military ranks if you were not atheist.

That is general simplistic overview, there is much more to write upon.

Sources. They are in my native tongue, do not know for English ones.

Savo B. Jović UTAMNIČENA CRKVA Stradanje sveštenstva Srpske Pravoslavne Crkve od 1945. do 1985. godine 2002.

Zdenko Radeljić Hrvatska u Jugoslaviji 1945. - 1991. 2006.

Miroslav Akmadža Katolička crkva u komunističkoj Hrvatskoj od 1945. – 1980. 2013.

Katrin Boeckh Vjerski progoni u Jugoslaviji 1944. – 1953.: staljinizam u titoizmu ČSP 2006.

I don't have the ability to answer this in full, but I will say you've posed a very broad question. There are a number of factors that influenced how religion is treated in each of the communist countries, and only a few of them have to do with communism directly. There's also a large influence of globalization, of cultural heritage, of the personal history of the founders of those governments, and more, and all played a major part in how each version of communism has come about. So are you limiting your answer to the strictly Communism-related factors, or are you asking in general about all the factors surrounding religious persecution/acceptance in the nations that became Communist?

Religion is rarely (if ever) banned in the so-called Communist states. Rather, there is just no national religion, people are free to practice their religion without interference from the State. The idea that Communists crack down on religious thought seems to have been spun by Capitalist governments to divide the religious and the communists. After all, Jesus has been described (rightly or wrongly) as a Socialist and the two areas have a lot of common ground.

Russia and Cuba have a huge history of Catholic belief, the architecture of which still stands today, if they have a problem with it they would have torn down the churches.