For the most part, I think the religious unbeliever will speak peace to his own soul on something less than biblical evidence of a work of grace from the Lord. Generally, and probably, his confidence will be based on something like a "decision for Jesus" or some other work motivated by self-preservation - don't forget the proud, reprobate Legion who were able to beg Christ for deliverance from immediate pain. Yet they were not one whit regenerated.

It has to be good to check the soul to see if there is a heartfelt reverence for the Lord, heartfelt thankfulness for His kindnesses, affectionate delight in His wise ways, tears for offending His Love, delight in Christ's glory in one's salvation, or even finding the mere thought of selflessly loving Him and receiving His Love to be lovely itself, even if such graces are only small or barely discernible and generally obscured by all the remaining darkness, rebellion, and unbelief.

Finally, we must know that our assurance rests wholly in the faithfulness of Christ's promise of forgiveness for those with a new heart of love for God, i.e., those who thirst after righteousness.