St. Paul is actually the perfect example of the traditional Christian approach to evangelizing pagans, Mohammedans, Jews or heretics. If, like some pagans, they admit nothing, we begin with the first principles of reason and natural law, showing that the existence of God can be known with certainty from the consideration of created things, as a necessary Cause from its contingent effects, as an intelligent Being deducible from the observed effects of intelligence in creation.
If, like Jews and Mohammedans, they recognize that God exists, then we show the necessity of believing in Christ, the divine proofs He offered of His mission, His absolute uniqueness, the fact of His Resurrection, His fulfilment of Messianic prophecy and the necessity for all to know and believe in Him.
And if, like heretics and schismatics, they profess to believe in Christ, but corrupt the dogmas of the faith or remain separated from Catholic communion, we prove to them, from Scripture and patristic Tradition the necessity of believing in the whole Faith and being subject to the See of Peter and the Roman Church.
But the reality of post-Vatican II ecuмenism was well summed by a person who even at the time observed something like, "To please the Orthodox, we deny or downplay the Papacy, to please the Protestants we derogate devotion to the Virgin Mother, to satisfy the Jews and Muslims we discard Christ ... and what is left?" This has been a complete inversion of right order, truly a diabolical disorientation. What should have been a proper approach oriented toward their conversion to the Faith or return to Catholic unity has been rather the path to indifferentism and apostasy.