Goodness. Sins do not separate us from God. Never have. Surely you remember that God actually came looking for Adam and Eve after Sin #1, and he called out to them... and He covered them in their shame and fear.
That's as bad as going for that old line that God can't be around sin. Was Jesus, God in flesh? Was He?
Did He not walk and talk with sinners every day? He even "touched" them.
Isaiah 59
59 Behold, the Lord's hand is not shortened, that it cannot save,
or his ear dull, that it cannot hear;
2
but your iniquities have made a separation
between you and your God,
and your sins have hidden his face from you
so that he does not hear.
3 For your hands are defiled with blood
and your fingers with iniquity;
your lips have spoken lies;
your tongue mutters wickedness.
4 No one enters suit justly;
no one goes to law honestly;
they rely on empty pleas, they speak lies,
they conceive mischief and give birth to iniquity.
5 They hatch adders' eggs;
they weave the spider's web;
he who eats their eggs dies,
and from one that is crushed a viper is hatched.
6 Their webs will not serve as clothing;
men will not cover themselves with what they make.
Their works are works of iniquity,
and deeds of violence are in their hands.
7 Their feet run to evil,
and they are swift to shed innocent blood;
their thoughts are thoughts of iniquity;
desolation and destruction are in their highways.
8 The way of peace they do not know,
and there is no justice in their paths;
they have made their roads crooked;
no one who treads on them knows peace.
9 Therefore justice is far from us,
and righteousness does not overtake us;
we hope for light, and behold, darkness,
and for brightness, but we walk in gloom.
10 We grope for the wall like the blind;
we grope like those who have no eyes;
we stumble at noon as in the twilight,
among those in full vigor we are like dead men.
11 We all growl like bears;
we moan and moan like doves;
we hope for justice, but there is none;
for salvation, but it is far from us.
12 For our transgressions are multiplied before you,
and our sins testify against us;
for our transgressions are with us,
and we know our iniquities:
13 transgressing, and denying the Lord,
and turning back from following our God,
speaking oppression and revolt,
conceiving and uttering from the heart lying words.