39 Finally, dialogue puts before the participants real and genuine disagreements in matters of faith. Above all, these disagreements should be faced in a sincere spirit of fraternal charity, of respect for the demands of one's own conscience and of the conscience of the other party, with profound humility and love for the truth. The examination of such disagreements has two essential points of reference: Sacred Scripture and the great Tradition of the Church. Catholics have the help of the Church's living Magisterium.
Source: Ut Unum Sint (Vatican.va)