Note Acts 2:44-45: "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."
But this was a unique situation that didn't last very long. We later see that elderly widows were to be financially provided for by a common church fund only if they had no family members in the Church who could privately support them (1 Timothy 5:3-16). Obviously, all members of the Church's congregations at this later time were not being provided for out of a common fund—only a select number in real need.
In considering Acts 2, we should note that Christians were being persecuted. Also, thousands of new believers, some from distant lands, had just been added to the Church at the Feast of Pentecost in Jerusalem.
No doubt many decided to remain in Judea at that time to learn more about their new faith and rely on one another through growing persecution rather than return to their homes far away. These people thus had an immediate need for food and lodging, and a voluntary pooling of resources took care of that.
The believers at the time felt extremely blessed, grateful, hospitable and generous. Many who had extra assets sold some of them to help finance the living expenses of others. The expression "all things in common" means this: "I love you, and therefore your needs are just as important to me as my own needs. I consider all that I have as being yours also."
However, keep in mind that they could not sell what they did not own. They were voluntarily selling some of their privately owned property so they could help others. This was charity, not communism. No one was compelled to sell his property, nor did anyone confiscate one's property or income to give it to others, as many governments do today.
Acts 4:32-35, which follows shortly after in time order, shows that the pooling of resources was still going on. The account of Ananias and Sapphira in Acts 5:1-11 adds further clarity. God did not execute judgment on these two for their refusing to share, but for their telling a lie to make themselves look good.
The apostle Peter asked Ananias, "While it [their possession] remained [unsold], was it not your own? And after it was sold, was it not in your own control?" The couple was not obligated either to sell their land or to give away the proceeds. Again, this was not communism or socialism.
The words of Jesus Himself should make it even clearer. In His parables of the workers in the vineyard in Matthew 20, He portrayed God as a vineyard owner paying different employees the same agreed-on amount even if they worked for less time.
The employees who worked longer thought it unfair. But the owner, representing God, replies to one: "Friend, I am doing you no wrong. Did you not agree with me for a denarius? Take what is yours and go your way. I wish to give to this last man the same as to you. Is it not lawful for me to do what I wish with my own things?" (verses 13-15).
To the final question here, communists and socialists, and those with such leanings, would answer no—since in those systems the community or state decides. Jesus' statement, while figurative of spiritual principles, is nevertheless a ringing endorsement of both private ownership and free market exchange without wage control. He was certainly no communist—and neither were His followers.