**But, regrettably, there are significant theological differences between Lutherans and those who call themselves Lutheran - significant enough to demand separate communions. **
To answer the OP’s question regarding Lutheran polity - Lutherans don’t require a centralized Magisterium to determine doctrine, as it is entirely self-evident in Scripture and the Confessions (which we view as the right reflection of Scripture). Should a church, either locally or at the Synodical level, strays from the Confessions, the remainder of the Lutheran Church, through its ‘ministerium,’ admonishes it and, if necessary, breaks fellowship. For instance, the LCMS, ELS and WELS no longer consider the ELCA to be an orthodox Lutheran body. Worldwide, other Lutheran bodies have done the same, including the largest Lutheran body in the world, the Mekane Yesus in Africa; it broke fellowship with the ELCA and the Church of Sweden and has sought fellowship with the LCMS. The Confessional Lutherans continue to meet and strive toward more visible unity.