God’s active presence in the world is synonymous with grace; they are substitutable in any context.
God is synonymous with “the good”, which is to say, synonymous with our sense of morality.
In suggesting that grace isn’t for all, active in all, sufficient to persuade people to strive to become better and more, then it’s to say God himself is not omnipresent and impotent rather than efficacious.
To suggest one can choose to believe is to suggest people do not desire “the good”. It’s to suggest God’s grace is not obvious, that goodness in all men is apart from God rather than a product of his presence in the world. It is to deny grace entirely; God’s active presence in the world.
Faith is merely being drawn to “the good” and responding to its nature, which implies we are responding to something obvious and universal to all people. Beliefs, whatever they may be, only pertain to descriptions of an experience of two of God’s gifts to humanity that all men enjoy and cannot earn, and a third gift we give ourselves.
That is, grace in the world that like a lover, draws us toward her, an encounter with her that makes us want to be our best selves, to believe in ourselves and to hope she lingers. And the gift we give ourselves is salvation because we can’t keep ourselves from doing something about it all because we now understand why the greatest of these is love.