Yes Divine grace is needed. But things are often about what the Eastern Orthodox call "phronema" a state of mind. Folks have mentioned non-Christians showing love etc. This is made possible because the Imago Dei that all humanity is created in. Unlike the West especially Protestantism like Calvinism, the Fall is seen less pessimistically in the East. Basically it damaged the Imago Dei but did' not destroy it.
But anyway back to Phronema a lot of things are about a state of mind, as far as living intentionally etc. It is the kind of attitude you bring to bear. This also is why some non-Christians much the chagrin of some Fundamentalists, can actually do well. They want to make everything about "Satanic counterfeits" etc. and overlook other passages that would undermine it like "a Kingdom divided cannot stand" etc. But the Bible has a lot to say about Phronema. I do not read passages like "Being Born Again" about having some kind of cathartic experience from praying the Sinner's Prayer (which is proof that you are saved) but about issues like Phronema, having your mind renewed in Christ etc. Basically you often have to unlearn some things of your past to embrace the way of God.
By the way on the issue of "believer" and "nonbeliever", a few years ago I blogged this (around Christmas time)....
Contemplating the Coming of the Magi
Sometimes we Christians like to divide the World into neat little categories. We like to have “believer" and "unbeliever", "Christian" and "non-Christian" and so forth Sometimes however real life doesn’t conform to such simplistic thinking. Because in the Gospels for example "Those outside Israel" sometimes could be "Close to the Kingdom of God", while those that were of natural Israel and devoutly practiced the old religion had "hearts that are far from God".
A good example of that is the coming of the Magi in the gospels. Those folks were mostly likely Zoroastrians from the region of Nineveh, (if we take the testimony of later Church historians seriously). These people had a close connection to the Jews during the first time of Exile. Some people think of Zoroastrians as "pagans" but they really have more in common with Monotheists in their beliefs than the other people of the pagan world. When we think about them we should realize that in the early Scriptures not all the people of God came directly from Abraham's line. Every so often we encounter someone like Melchizedek or Job. Even Balam the prophet, before he became corrupt was seen as being a "prophet of God".
When we contemplate the Magi, we should not forget that Abraham himself came from their region a few millennia previously. In fact, the name Hebrew is said to derive from this culture. It comes from an ancient Akkadian or Proto-Aramaic word meaning “They that dwell beyond the River” (Euphrates).
We therefore should not be surprised why the events recorded in the Book of Jonah take place. We have sayings “what comes around goes around”. And that certainly is true with the Kingdom of God itself. Or as scripture says, in Ecclesiastes 11: 11 “Cast your bread upon the waters, for you will find it after many days.”
God who stands beyond Time itself knows all things. Besides being the place where the ancient Hebrews came from, he also knew it as a place that held great future promise for Christianity.
Isaiah 19: 23In that day there will be a highway from Egypt to Assyria, and the Assyrians will come into Egypt and the Egyptians into Assyria, and the Egyptians will worship with the Assyrians. This is one of those prophesies that already has been at least partially fulfilled. For the Coptic Christians and Syriac Orthodox Christians have been worshiping Christ and been in Communion with each other for nearly two millennia.
It was the place that saint Thaddeus (aka Jude the apostle) later missionized and turned into an Apostolic See that stretched forth all the way to India and China, which lasted until the late middle ages and continues today (although greatly diminished). Besides that, this region has been the home of great saints like Isaac of Nineveh (Saint Isaac the Syrian).
It is of course this same region and the Christians that dwell therein that very much need our prayers. For they struggle everyday against persecution and genocide by Islamic Fundamentalist groups like ISIS.