Vatican II declares: “All men are called to this catholic unity, which prefigures and promotes universal peace” (Lumen gentium, art. 13).
No exceptions. Everyone is called. Why? First, because of the means of salvation, all of which are available only in the Catholic Church (Unitatis redintegratio, art. 3). Second, because God wills all to be one and to come together in the one body of his one Church. This unity will foster true peace. (Of course, there are always members of the Church that are in fact dead to Christ and to his calling.) So that, Lumen gentium, art. 14, the Catholic Church is necessary for salvation.
The Church as a whole accepts these truths and works towards the accomplishment of this goal. Hence, there most certainly is an institutional commitment to the conversion of everyone to the Catholic Church: “The Church prays and likewise labors so that into the People of God, the Body of the Lord and the Temple of the Holy Spirit, may pass the fullness of the whole world….” LG, art. 17.
Or, as the Decree on Ecumenism declares: Jesus entrusted the Church to the College of Bishops “in order to establish on earth the one Body of Christ into which all those should be fully incorporated who belong in any way to the people of God” (UR, 3).
Evangelization must always be done in charity, for its aim is charity. Charity requires prudence, for which there is no set of laws that can suffice. Thus, we must put on the mind of Christ in order to discern what is the best way forward in this one, universal, and irrevocable missionary mandate of the entire Church to the entire world.