What is the Commonwealth of Israel?
I assume you are referring to the small religious group that calls itself "Twelve Tribes: The Commonwealth of Israel." It was started in the 1970's by Gene Spriggs in Chattanooga, Tennessee. It contains an odd blend of beliefs arising from its attempt to blend Old and New Testament beliefs.
Like the Messianic Jews, The Commonwealth people build much on what is not in the Scriptures. They insist on calling the Christ "Yahshua" because they believe that it is closer to how Jesus' name would have been pronounced in Hebrew. Thus they reject the idea that the New Testament was originally written in Greek by the inspiration of the Holy Spirit. Interestingly, they admit that they don't know exactly what Jesus' Hebrew name would have been or how it would have been pronounced, but this is what they settled on.
Their blending causes them to worship on the Sabbath and keep the Old Testament dietary laws. Thus when the Old and New Testament differ, they will pick which of the laws they prefer to follow.
They believe the church is to be organized in twelve regions, one representing each tribe of Israel. It is based on a misunderstanding of Paul's words in Acts 26:7 and assigning a literal meaning to the mention of the twelve tribes in Revelation, a book stated to be written in figurative language.
[See: An Introduction to Revelation ]
They believe in baptism as a part of the plan of salvation, but the community determines who is a candidate for baptism. They have to be first convinced that the person truly believes their teachings.
[See: Topical Index on Salvation ]
Members are required to join in existing communities of families. These families deny all worldly ties, except for each other, and in live in a communal style (all things are own by the community and not by the individual).
[See: Economic Systems ]
They are also a Premillennialist group. They believe Jesus is returning to reign on earth, but only after they establish a purified group of followers for him to lead. They also believe in a second chance for people who never heard the Gospel of Christ, but tried to live a "good" life to the best of their ability. Thus people are divided into three groups. The wicked who reject Jesus, the good but ignorant people who get a second chance in the millennial reign, and the holy who have believed and been purified by persecutions.