With the coming of Jesus of Nazareth (the theologians call this the "incarnation: God in the flesh"), the emphasis on both the character of God and how we relate to God changed dramatically.
The Old Testament emphasized the holiness of God and therefore our holiness. Holy God was not to be touched or even looked upon by sinful people. However, with the coming of Jesus the emphasis changed from holiness to compassion.
Jesus purposefully recast the wording of the Old Testament law, from “You shall be holy for I the Lord your God am holy” (Leviticus 19:2) to New Testament grace: “Be compassionate, just as your Father is compassionate” (NEB Luke 6:36).
In Jesus, we see the compassion of God embodied, and now His compassion rather than our purity is the foundation of our relationship with Him.
God, who formally forbade anyone to touch His holy things (mountain, arc, etc.), now touches people and people touch Him. No longer is God inaccessible, residing on a forbidden mountain or cloistered behind the veil of the Temple. Now sinful people touch Holy God. (Moses would be amazed. So should we!)
Jesus, the incarnate God, now fellowships and dines with sinners. He told the religious and self-righteous that it was for the sick not the well, for sinners not the righteous that He came. Jesus' enemies criticized Him because He was known as "a friend of sinners" (Luke 7:34). Aren't we glad that He is!
You may not be very holy, but by trusting God to be a God of love, mercy, and grace, you are still welcome at His table to dine with your Friend. You can touch Him, and He will touch you.