Jesus gave the church a commission, and that is to teach what he taught. Even when Protestants broke away from the Church to form other denominations, the Catholic/Orthodox churches stayed as close as possible to traditional Apostolic teachings. Many non-Catholic Christians dismiss tradition.
While the Catholic/Orthodox Church does acknowledge the Covenants God has with others, it sees its job to teach as Christ taught. The Catholic/Orthodox do not teach Judaism, Hinduism, Buddhism, Muslim, or any other Christian denomination. The Church was told to teach as Christ taught. Still, the Church has humility. Simply because the Church is not able to bring all persons to Jesus in this way, it does not lessen the responsibility for the Church to follow Christ's ways and trust all who are not of Christ are in the hands of a loving, merciful God.
I will note that those who teach, "Believe in Christ or go to hell" more than likely believe they are following Christ's commission more closely. It is probably true that my trust that God, in His love and mercy, will bring in all others who wish to be with him, may be over-emphasized. Still, I point to the Parable of the Vineyard.