The Soviet Union was largely unsuccessful in reducing religiousness by 1943, when it began to scale back its campaign against organized religious groups like the Russian Orthodox Church (ROC) - however, its efforts weren't entirely in vain. At the turn of the 20th century, it's believed that around 90% or more of the population "practiced" religion - not only were they believers, but they went through with the proscribed rituals such as confessions and attending church weekly. In the 1937 Soviet census the number of people identifying as "religious" was 57%. At its face this number represents a decline, but in the context of when the census took place - the Great Terror, where openly declaring your religiousness could make you a target of repression - it should be read as a failure of state policy. If 57% of the population was willing to openly express their religiousness to state agents despite the serious risks, a far larger portion may have also remained faithful but not as open.

On the other hand, you have a number of qualitative studies which suggest that there was significant anti-religious behavior "from below". In the countryside many bedniaks - a word literally referring to a poor peasant but usually used to refer to any pro-Soviet peasant - advocated against religion without direct state instruction throughout the 1920s. They were usually young people, Red Army veterans, and people with trades that created more interaction with cities, such as craftsmen. Older peasants would refer to young people running amok as "Komsomol-hooliganism" - the Komsomol being the Bolshevik youth organization. During collectivization, this "hooliganism" took the form of raiding and robbing churches, attacking priests, etc. Stalin actually condemned this behavior in his March 1930 Pravda article "Dizzy with Success: Concerning Questions of the Collective-Farm Movement", stating that:

I have nothing to say about those "revolutionaries"... who begin forming an artel by taking the bells from churches. [Italics mine]

While obviously Stalin was no defender of religion, the point that gets across is that anti-religious behavior was often spontaneous, violent, and undesirable even for state authorities. So while the Soviet state didn't reduce religiousness significantly, there undeniably was some organic decline even in the countryside.

Sources:

Fitzpatrick, Sheila, "The Question of Social Support for Collectivization"

Merritt, Steven M., Stalin's Holy War: Religion, Nationalism, and Alliance Politics, 1941-1945

Kenworthy, Scott M. "Rethinking the Russian Orthodox Church and the Bolshevik Revolution"

Stalin, Joseph V. "Golovokruzhenie ot Uspekhov: K Boprosam Kolkhovnogo Dvizheniya"

Young, Glennys, Power and the Sacred in Revolutionary Russia: Religious Activists in the Village