Sadly not many, though the answer is more complex. I'd not really consider the liberal Catholics I know to be Catholics in any meaningful sense, just liberals who might borrow an aesthetic.
A lot of conservative Catholics seem to hold ideals that would be closer to what Communists would find to be agreeing: an emphasis on social justice, mistrust of the government and business in general, desire to help the poor, etc. Problem is their image of Communism is anti-Catholic militias during the Spanish Civil War, plus it's pretty easy for them to fall into a reactionary aesthetic.
A great deal of traditionalist, conservative Catholics want the church to *be* something, quite a few confessed that they want it to be a cause, something worth dying for, rather than a mundane part of everyday life. Sadly a few have adopted some Zig Forums-tier "we need another Crusade" meme in hopes that the church would exercise some strength and call people to sacrifice themselves for a "higher" cause. In my opinion, if we do need another crusade, it should be a crusade against Capitalism, with a new holy order of chivalric Knights being the first to truly deserve the title in their battle against the bourgeoisie.
The idea that religion would dissipate under communism rests on two beliefs: that it exists merely to "explain the unexplainable" and as a temporary reprieve of peoples' suffering. It's normal to hear some atheists argue that in luxurious first world nations, people have "better things to do with their free time than go to church." If we think about it, after all, why would someone who has enough time to do *anything* go to a mass?
Well to the charge that God can only exist in the shadows and is dispelled as soon as we shine the light of science upon something, I argue that there's nothing inherently disproving of God in learning the movement of atoms, the atheist may see such a thing and ask "Well where's God?" But the fact is no one really knows what to look for when looking for God, however it's almost as if some of these internet atheists think they should be able to get a high-powered telescope, look up at the stars, and see an old man floating on a cloud.
The bible never existed as a scientific manual, it was never meant to instruct people in the material functioning of the world and be used as the building block of all later human innovation, it existed first and foremost as a spiritual text, not merely a guide on good behavior but a way of understanding the world and man's place within it. Some may sneer that the concept of humans being born with original sin or as "inherently evil" is a pessimistic, harsh, and cruel understanding of things, yet with that understanding comes a certain kind of humility and forgiveness. The call of Catholicism is ultimately to forgive and redeem ourselves and those around us. communism would solve a great deal of social ills, but I don't think this is any rebuke of "original sin", rather that man's "evil" in the true Augustinian sense, is a deficiency in our willingness to do good, it's why communism is something that has to be fought for rather than evolved into.
Now, in regards to existing merely to solve physical suffering and that, were work to be abolished, people would be less religious, to this I argue that our peasant ancestors in medieval Europe actually had numerous days where they didn't need to work. Some have said they only had to work half the year in fact, however their religious beliefs didn't falter with a great deal of time off, if anything they were stronger than ever.
I imagine the constant, repetitive grind of Capitalism played its part in crushing mass attendance, after all why would anyone go to mass on their one Sunday off after 5 days of mentally exhausting or physically backbreaking labor?
Communism would open the world up, it would reduce the time we're working, people would be free to travel and explore. The religious caste, the priests, the churches, now free from the struggle for resources and material power, would be more than capable of debating religious matters and producing some truly great thinkers. It would not surprise me, I think, if we saw a whole host of new saints and miracles once mankind's been freed from capitalism.