I would just add “and is baptized.”
But yeah, reducing Christianity to simply its morality/ethics misses the point and empties it of its transcendence.
As the Scriptures say, “without faith it is impossible to please God.” That being said, doing good to one’s neighbor can be itself a participation in grace that helps put one on the path towards faith and salvation, as Pope Francis taught in his first encyclical, speaking about unbelievers:
Pope Francis, Lumen Fidei
To the extent that they are sincerely open to love and set out with whatever light they can find, they are already, even without knowing it, on the path leading to faith…Anyone who sets off on the path of doing good to others is already drawing near to God, is already sustained by his help, for it is characteristic of the divine light to brighten our eyes whenever we walk towards the fullness of love.