The only thing that matters is whether they do good in solidarity with jesus.

Jesus was the only person who ever merited salvation from god, since he had no sin of his own, and so the remission of sin is done through a person vicariously receiving what jesus has earned. vicarity only exists in solidarity, and so a person only receives what jesus earned when they do good for the same purpose that jesus did what he did for.

now then, the agnostic and the "other believer"? maybe they can do this. the western atheist, though, actively denies christ. he openly and directly denies christ. He will go to hell, because nothing he does can ever be in solidarity with christ, as his whole identity revolves around his denial of christ.

the agnostic might do good to the same ends of christ, and thereby merit salvation. he knew not, but it might be made known to him by god.

the "other believer", who knows nothing of christ, but tries to do good for the same reason christ did, he too might receive christ's vicarious merits. He does not deny, and so he may receive that which he never knew that he asked for.

the atheist, though? he always denies christ. and so all of his works are like a fool who continuously assembles and disassembles a motherboard in his basement, thinking himself to have the merits of a person working in a computer factory -- he does the same material work, but without solidarity with Dell, he ain't gettin' paid for it.