Without the Pope to settle disputes, how does the faith decide what's true if bishops disagree on something?
While there is indeed historical precedent for the Bishop of Rome's role as a sort of 'Final Court of Appeals' for specific causes and cases, the papal office has never been the only (or even the best) way to firmly settle disputes within the Church.
The Catholic Church has a long history of Councils, both local, regional, and ecumenical who have historically been used to settle some of the most important and divisive issues within the Church. These councils involved the Bishops, Clergy, and leaders from the whole church to come together in Synod to settle great matters of debate.
The Councils even had the authority to restrain or judge the occupant of the Papal Office, as seen in the Council of Constance (1414-1418) which helped to settle the Western Schism. Other examples include the very first ecumenical councils such as Nicaea which settled Christological debates.
The Church has always been a community, and it is in coming together as a community to discuss, debate, and grow that we move forward as Christians together. That doesn't mean that every member of a Council or Synod has to agree, but that they agree - as part of a Christian body - to accept the judgement of the Church insofar as it accords with history, theology, and continuity with our ancient traditions.