OT clean and unclean
The ideas of clean and unclean from the Old Testament are also used in the New Testament.
The word "clean" doesn't refer to sin. For example, it is not a sin to give birth yet that makes you unclean.
Speak unto the children of Israel, saying, If a woman have conceived seed, and born a man child: then she shall be unclean seven days; according to the days of the separation for her infirmity shall she be unclean. (Leviticus 12:2)
The word "clean" can mean wicked or evil.
Just as sprinkling the blood of animal sacrifices in the Old Testament cleanses the worshippers, so also, sprinkling the blood of Jesus on believers cleanses us of our sin and puts us in right standing with God.
Moreover he sprinkled with blood both the tabernacle, and all the vessels of the ministry. And almost all things are by the law purged with blood; and without shedding of blood is no remission. (Hebrews 9:21,22)
Notice that Christians are not literally sprinkled on their physical body with the physical blood of Jesus but, rather, this occurs with the spiritual blood of Jesus on our spiritual body. Just as Abel's blood spilled on the ground, so also did the blood of Jesus.
I can imagine that in the spiritual realm there is some sort of ceremonial sprinkling of the blood of Jesus over us, to cleanse us. Usually it's thought of as all figures of speech but doing this renders it unintelligible.
I was in a meeting of Baptists once in which they were getting all excited about the blood of Jesus, but I didn't know what they were talking about because even though his blood was not physically present, they acted as if it was. Somehow Jesus took his blood and applied it to the doorpost on the Passover and the Mercy Seat in the tabernacle. This could only happen in the spiritual realm — and so it did.
And one of the elders answered, saying unto me, What are these which are arrayed in white robes? and whence came they? And I said unto him, Sir, thou knowest. And he said to me, These are they which came out of great tribulation, and have washed their robes, and made them white in the blood of the Lamb. (Revelation 7:13,14)
The confusion of the concepts of holiness and cleanness leads to the idea that the body is bad. In Old Testament times, getting leprosy made you unclean, but there is nothing sinful about getting leprosy. The blood of sacrifices was used to cleanse people and sacred objects.
It is not a sin to have leprosy, therefore, the word "clean" does not mean sin.
The religious leaders of Jesus' day were obsessed with rituals such as washing hands and cups; these practices having support from the Old Testament. Washing was a way of becoming clean with God and physical cleanliness was tangled-up with spiritual cleanliness. Jesus corrects them: that the condition of the heart is the important thing, not mere ritualistic observances. But rejecting all rituals as having no value is wrong also; Jesus doesn't suggest they change their religious lifestyle, only that they have a clean heart before God. Thus, Catholic and Orthodox ceremonies and rituals have great benefit when mingled with faith; it is wrong to reject such as these out of hand.