What was the Early Church belief on socialism … ?
- Concepts like socialism and communism are recent political terms that didn't exist during biblical times.
- Except within large families or small close-knit villages, it's unlikely anything resembling these ideas would have even existed.
- Even had they existed, there would be no practical purpose for them; people couldn't simply form a new political party dedicated to overturning the entire economic structure of the Roman Empire.
… and did they practice it?
The only reason for even suspecting that this might be true is the text that is quoted in the question and which is frequently quoted by those that want a proof-text that Jesus supported socialism, communism, or communalism.
No personal property, having all things in common, distributing according to need certainly, all sound like communal living.
But this claim totally ignores the context of the quotation.
It is purely the product of eisegesis, reading what one already believes into the text.
In fact, it is quite easy to disprove the idea using another proof text:
For you yourselves know how you ought to follow us,
for we were not disorderly among you;
nor did we eat anyone’s bread free of charge,
but worked with labor and toil night and day,
that we might not be a burden to any of you,
not because we do not have authority, but to make ourselves an example of how you should follow us.
For even when we were with you, we commanded you this: If anyone will not work, neither shall he eat.
— 2 Thessalonians 3:7–10
This is definitely not the kind of example one would set for a socialist lifestyle.
But that scripture by itself isn't definitive "proof", any more than was the original quotation in the Question.
Instead of eisegesis, the best way to properly understand scripture is through exegesis, determining truth from out of the text, by looking at everything in context, considering people's motives and viewpoints, and using abductive reasoning to eliminate explanations that create more questions than they answer.
Acts 4:32–35, quoted in the Question, is simply a recap of what is described two chapters earlier:
Now all who believed were together, and had all things in common,
and sold their possessions and goods, and divided them among all, as anyone had need.
— Acts 2:44–45
Why did they do that?
First, consider what happened just before that:
Then those who gladly received his word were baptized; and that day about three thousand souls were added to them.
And they continued steadfastly in the apostles’ doctrine and fellowship, in the breaking of bread, and in prayers.
— Acts 2:41—42
Instead of consisting of a few long-time disciples, the community had suddenly expanded into thousands of people, all learning, living, eating, and praying together.
This rapid expansion immediately followed the beginning of the church of God during Pentecost following the Crucifixion described earlier in the same chapter:
When the Day of Pentecost had fully come, they were all with one accord in one place.
And suddenly there came a sound from heaven, as of a rushing mighty wind, and it filled the whole house where they were sitting.
Then there appeared to them divided tongues, as of fire, and one sat upon each of them.
And they were all filled with the Holy Spirit and began to speak with other tongues, as the Spirit gave them utterance.
And there were dwelling in Jerusalem Jews, devout men, from every nation under heaven.
And when this sound occurred, the multitude came together, and were confused, because everyone heard them speak in his own language.
Then they were all amazed and marveled, saying to one another, “Look, are not all these who speak Galileans?
“And how is it that we hear, each in our own language in which we were born?
“Parthians and Medes and Elamites, those dwelling in Mesopotamia, Judea and Cappadocia, Pontus and Asia,
“Phrygia and Pamphylia, Egypt and the parts of Libya adjoining Cyrene, visitors from Rome, both Jews and proselytes,
“Cretans and Arabs—we hear them speaking in our own tongues the wonderful works of God.”
— Acts 2:1–11
This is where most of the three thousand new Christians came from; not from Jerusalem's inhabitants, but from Jews visiting from throughout the Roman Empire.
Whether they had come to Jerusalem for a Pentecost pilgrimage or on business, they were all visitors, all expecting to return home in the near future.
But now unexpectedly, they had been given a taste of God's truth and wanted more; they couldn't simply drop it and go home.
(It seems likely that this was God's plan, for these foreign Jews to be converted and to spread the Gospel when they do finally return to their own lands.)
Instead, they all wanted to stay and learn for as long as reasonably possible.
But many of them couldn't afford to stay any longer, and many of those that were rich enough didn't have access to any of their money (no ATMs or e-transfers in those days).
So, those that did have access to money, or to possessions that could be sold, donated what they had to the common cause.
They themselves wanted to stay and learn, so they understood how much everyone else also wanted to stay.
And everyone understood the mission they had suddenly been assigned, to spread the Gospel message around the world.
Yes, they were living communally, but clearly this was a temporary arrangement, out of necessity rather than choice.
As the quotation from Paul's second letter to the Thessalonians confirms, the new Christian communities that arose from the resulting evangelism did not practice a socialist lifestyle — "If anyone will not work, neither shall he eat.".