Thou - shalt wash them - This was done emblematically, to signify that they were to put away all filthiness of the flesh and spirit, and perfect holiness in the fear of God; 2 Corinthians 7:1.

unto the door

Exodus 26:36 And you shall make an hanging for the door of the tent, of blue, and purple, and scarlet, and fine twined linen...

Exodus 40:28 And he set up the hanging at the door of the tabernacle.

Leviticus 8:3-6 And gather you all the congregation together to the door of the tabernacle of the congregation...

wash them

Exodus 30:18-21 You shall also make a laver of brass, and his foot also of brass, to wash with...

Exodus 40:12 And you shall bring Aaron and his sons to the door of the tabernacle of the congregation, and wash them with water.

Leviticus 8:6 And Moses brought Aaron and his sons, and washed them with water.

Leviticus 14:8 And he that is to be cleansed shall wash his clothes, and shave off all his hair, and wash himself in water, that he may be clean...

Deuteronomy 23:11 But it shall be, when evening comes on, he shall wash himself with water: and when the sun is down, he shall come into the camp again.

Ezekiel 36:25 Then will I sprinkle clean water on you, and you shall be clean: from all your filthiness, and from all your idols, will I cleanse you.

John 13:8-10 Peter said to him, You shall never wash my feet. Jesus answered him, If I wash you not, you have no part with me...

Ephesians 5:26 That he might sanctify and cleanse it with the washing of water by the word,

Titus 3:5 Not by works of righteousness which we have done, but according to his mercy he saved us, by the washing of regeneration...

Hebrews 10:22 Let us draw near with a true heart in full assurance of faith, having our hearts sprinkled from an evil conscience...

1 Peter 3:21 The like figure whereunto even baptism does also now save us (not the putting away of the filth of the flesh...

Revelation 1:5,6 And from Jesus Christ, who is the faithful witness, and the first begotten of the dead, and the prince of the kings of the earth...

Sixth Day. Holiness and Glory.
Who is like unto Thee, O Lord! among the gods? Who is like unto Thee, glorious in holiness, Fearful in praises, doing wonders? Thou in Thy mercy hast led Thy people which Thou hast redeemed: Thou hast guided them in Thy strength to the habitation of Thy holiness ... The holy place, O Lord, which Thy hands have established.' --Ex. xv. 11-17. In these words we have another step in advance in the revelation of Holiness. We have here for the first time Holiness predicated of God Himself. He …
Andrew Murray—Holy in Christ

Exodus
The book of Exodus--so named in the Greek version from the march of Israel out of Egypt--opens upon a scene of oppression very different from the prosperity and triumph in which Genesis had closed. Israel is being cruelly crushed by the new dynasty which has arisen in Egypt (i.) and the story of the book is the story of her redemption. Ultimately it is Israel's God that is her redeemer, but He operates largely by human means; and the first step is the preparation of a deliverer, Moses, whose parentage, …
John Edgar McFadyen—Introduction to the Old Testament