I think you are correct that a Trinitarian understanding of God is necessary to be called a Christian. It is one of the reasons why Mormons are not Christians and Mormon baptisms are not recognized by the Catholic Church, even though they talk about the Trinity. The term means something very different to them; the Mormon Trinity is three beings who are not equal and not of one substance.
Pope Francis and the whole Catholic Church believe that the basis for marriage, family, and human dignity are knowable from reason alone. There is no reason you have to be Catholic, Christian, pagan, Buddhist, Muslim, Hindu, or atheist to reach the same conclusion: that marriage and family are the basis of any society. The World Meeting of Families included people from many other faiths to emphasize that, and that event was the main purpose of his trip to the US in the first place.