Ps 53:1 The fool has said in his heart, “There is no God.” They are corrupt, and have done abominable iniquity; there is none who does good.
:2 God looks down from heaven upon the children of men to see if there are any who understand, who seek God.
:3 Every one of them has turned aside; they have together become corrupt; there is none who does good, no not one.
:4 Have the workers of iniquity no knowledge, who eat up my people as they eat bread, and do not call upon God?
:5 There they are in great fear where no fear was, for God has scattered the bones of him who encamps against you; you have put them to shame, because God has despised them.
:6 Oh, that the salvation of Israel would come out of Zion! When God brings back the captivity of His people, let Jacob rejoice and Israel be glad.
This is headed as Folly of the Godless, and the Restoration of Israel.
This is almost the same as Psalm 14. The fool is the person who lives like there is no God. Not the person who doesn't believe at all there is a God. Left to ourselves we all are lost. That is David's point. The only refuge for the person who has offended God is to run to God. When we sincerely seek Him for forgiveness He gives it.
Since it was included twice it must be important. We should really meditate on it.
Michael Wilcock said: Trust God, and you have nothing to fear. Ignore Him, and you have everything to fear.