If, according to doctrine, those who do not claim to love God are bound for Hell, then loving their fellow men would not save them.
But the angel got it right -
Matthew 25 37
"Then the righteous will answer Him, 'Lord, when did we see You hungry, and feed You, or thirsty, and give You something to drink?
'And when did we see You a stranger, and invite You in, or naked, and clothe You?
'When did we see You sick, or in prison, and come to You?
"The King will answer and say to them, 'Truly I say to you, to the extent that you did it to one of these brothers of Mine, even the least of them, you did it to Me.' "
The non-religious are as likely to do these things as those who profess to love the Lord.