Who or what shall separate us from God?
If sin separates us from God, and it does, then it should be handled seriously and addressed without compromise.
If sin separates us from God before repentance, and it does, then sin certainly separates us from God just the same if sin is committed after one is "saved".
Again, When a righteous man doth turn from his righteousness, and commit iniquity, and I lay a stumblingblock before him, he shall die: because thou hast not given him warning, he shall die in his sin, and his righteousness which he hath done shall not be remembered; but his blood will I require at thine hand. Ezekiel 3:20
Being saved from sin does not give anyone a license to sin. That thinking is ridiculously illogical and not at all Biblical.
If God will not share His glory with anyone or anything He certainly will never share it with our sin.
I am the Lord: that is my name: and my glory will I not give to another, neither my praise to graven images. Isaiah 42:8
For mine own sake, even for mine own sake, will I do it: for how should my name be polluted? and I will not give my glory unto another. Isaiah 48:11
People are quick to say that nothing can separate us from God once we are saved and somehow they even believe that sin all of a sudden becomes less severe and that even sin cannot separate us from God.
They cite the following as proof:
Who shall separate us from the love of Christ? shall tribulation, or distress, or persecution, or famine, or nakedness, or peril, or sword?  Nor height, nor depth, nor any other creature, shall be able to separate us from the love of God, which is in Christ Jesus our Lord. Romans 8:35,39
But they fail to realize that God never changes and this absolutely includes His abhorrence towards sin. The reference in Romans does not include one's personal sin and for good reason...
Unrepentant sin can and does separate us from God.
But your iniquities have separated between you and your God, and your sins have hid his face from you, that he will not hear. Isaiah 59:2
I tell you, Nay: but, except ye repent, ye shall all likewise perish. Luke 13:3
So we must stop diminishing the severity of sin and address it head-on and without compromise.
Them that sin rebuke before all, that others also may fear. 1 Timothy 5:20
Unrepented sin separates us from God with no exceptions...
So to address the initial question, "who shall separate us" we should also be asking "who shall ascend and abide...?"
Who shall ascend into the hill of the Lord ? or who shall stand in his holy place? He that hath clean hands, and a pure heart; who hath not lifted up his soul unto vanity, nor sworn deceitfully. He shall receive the blessing from the Lord , and righteousness from the God of his salvation. Psalm 24:3-5 Lord , who shall abide in thy tabernacle? who shall dwell in thy holy hill? He that walketh uprightly, and worketh righteousness, and speaketh the truth in his heart. He that backbiteth not with his tongue, nor doeth evil to his neighbour, nor taketh up a reproach against his neighbour. In whose eyes a vile person is contemned; but he honoureth them that fear the Lord . He that sweareth to his own hurt, and changeth not. He that putteth not out his money to usury, nor taketh reward against the innocent. He that doeth these things shall never be moved. Psalm 15:1-5