I don't know much about that, but a brief search on the Web produced this:
When the Pilgrims created the Mayflower Compact, it lacked one important thing--authorization by the English government. The Mayflower Compact was a "quick fix", but even the Pilgrims knew they would need the authority of the English government behind them if they wanted to continue living at Plymouth. When news from Plymouth returned to England in May, 1620 along with the Mayflower, the Merchant Adventurers (stockholders in the Plymouth Plantation) led by John Peirce went to the Council of New England to get the Pilgrims the rights to live and establish a government of their own at Plymouth. The result was the 1621 Pierce Patent, which in a sense superceeds the Mayflower Compact.
I never had the impression that religious beliefs of the Pilgrims included communalism, at least not to the extent practiced later in history by groups such as the Shakers or the Harmonists. But it does make sense that such conditions would have been agreed to prior to their journey, simply as a practical matter for safely establishing a colony in a remote wilderness.