An objective mortal sin is a knowingly chosen act of the human person, an act which is objectively gravely immoral. An actual mortal sin is an objective mortal sin which is committed with full knowledge of its grave immorality and full deliberation (full freedom of choice).
Suppose that an act is objectively only a venial sin, or objectively not a sin at all. If a person mistakenly thinks that the act is gravely immoral, and commits that act with full knowledge and full deliberation, the act is an actual mortal sin. For it is always gravely immoral to freely and knowingly choose to do what you yourself think to be gravely immoral.
In this fallen sinful world, many persons commit objective mortal sins without full knowledge of the gravely immoral of the act. Their choice is an objective mortal sin, but not an actual mortal sin.
Only actual mortal sin deprives the soul of the state of grace. Only unrepented actual mortal sin deserves eternal punishment in Hell.
Therefore, persons who are unrepentant from objective mortal sins, which are not also actual mortal sins, can be saved even if, unfortunately, they do not realize their error and give up those sins prior to death. As long as the individual entered the state of grace by some form of baptism, and either never committed an actual mortal sin or at least repented from all actual mortal sins, that person will die in the state of grace and have eternal life.
This implies that atheists can be saved without converting to belief in God. Their refusal to believe in God might not be an actual mortal sin, and therefore they might be saved. They can enter the state of grace by an implicit baptism of desire and return to the state of grace after any actual mortal sin by an act of implicit perfect contrition. Some atheists may be guilty to the extent of actual mortal sin for their rejection of God and religion; other atheists might be in a state of invincible ignorance.
The same can be said about other sins. Homosexuals who are sexually active or in a legal same-sex marriage can possibly be saved without giving up this sinful behavior — if they are invincibly ignorant of the gravely immoral of their actions and not guilty (or at least repentant) from other types of grave sin. The state of grace can be possessed by persons who unfortunately do not realize that their actions are gravely immoral. This includes various sexual sins, the divorced and remarried, cohabitating couples, and other sins. Some persons might be guilty to the extent of actual mortal sin for their sexual sins; others might be in a state of invincible ignorance.
However, there are limits to invincible ignorance. Some grave sins are so severe that they cannot be mistaken by a sincere conscience for morally permissible acts. In all cases, God is the judge over each person and their conscience.
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