That may be your philosophy, but it's not what Jesus said. He told his disciples to take the gospel to all men: "Go, therefore, and make disciples of all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Spirit, teaching them to observe all that I have commanded you" (Mt 28:18-19).
This is known as the Great Commission, not the Great Imposition.
Jesus commanded his followers to make others Christians through preaching and baptism. We must all, in one capacity or another, be evangelists and present the truth of Christ to those who don't yet accept it. In so doing, we aren't imposing anything on them. Christ wants a free acceptance of himself and his message.
Evangelization is not an imposition but an act of charity. Through it the whole truth about God and man is made known to people in need. Those outside the Church hear the message of Christ the Savior and become united with him in his Church, his Mystical Body.
"Live and let live" is a false philosophy. It reduces to Cain's question, "Am I my brother's keeper?" In things spiritual as well as things material, we are indeed our brother's keeper.