How is the idea of the ritual purity implemented in the Catholic Church?
First of all we must see what ritual purity in Judaism.
The Hebrew Bible mentions a number of situations when ritual purification is required, including during menstruation, following childbirth (postpartum), sexual relations, nocturnal emission, unusual bodily fluids, skin disease, death (corpse uncleanness), and animal sacrifices. The oral law specifies other situations when ritual purification is required, such as after performing excretory functions, meals, and waking. The purification ritual is generally a form of water-based ritual washing in Judaism for removal of any ritual impurity, sometimes requiring just washing of the hands, and at other times requiring full immersion; the oral law requires the use of un-drawn water for any ritual full immersion - either a natural river/stream/spring, or a special bath (a Mikvah) which contains rain-water.
These regulations were variously observed by the ancient Israelites; contemporary Orthodox Jews and (with some modifications and additional leniencies) some Conservative Jews continue to observe the regulations, except for those tied to sacrifice in the Temple in Jerusalem, as the Temple no longer fully exists. These groups continue to observe many of the hand-washing rituals. Of those connected with full ritual immersion, perhaps the quintessential immersion rituals still carried out are those related to nidda, according to which a menstruating woman must avoid physical contact with her husband, especially avoiding sexual contact, and may only resume contact after she has first immersed herself fully in a mikvah of living water seven days after her menstruation has ceased.
Tumat HaMet ("The impurity of death"), coming into contact with a human corpse, is considered the ultimate impurity, one which cannot be purified through the waters of the mikvah. Tumat HaMet required purification through sprinkling of the ashes of the Parah Adumah, the Red Heifer. However, the law is inactive, since neither the Temple in Jerusalem nor the red heifer is currently in existence, though without the latter, a Jew is forbidden to ascend to the site of the former. All are currently assumed to possess the impurity of death. However, someone who is a Kohen, one of the priestly class, is not allowed to intentionally come into contact with a dead body, nor approach too closely to graves within a Jewish cemetery.
Purification was required in the nation of Israel during Biblical times for the ceremonially unclean so that they would not defile God's tabernacle and put themselves in a position to be cut off from Israel. An Israelite could become unclean by handling a dead body. In this situation, the uncleanliness would last for seven days. Part of the cleansing process would be washing the body and clothes, and the unclean person would need to be sprinkled with the water of purification. - Ritual purification
It is obvious that not having ritual purity is not the same thing as not being in the state of sin. Christ has died once and for all that we may have eternal in abundance. He gave the Apostles the power to forgive actual sin committed by the faithful.
That said there is a vestige remaining within the Church of performing some sort of ritual purity.
The idea of ritual purification still has a few remnants in the Roman Ritual (Rituale Romanum) and in the liturgy in general.
The churching of women is an example of this.
A blessing given by the Church to mothers after recovery from childbirth. Only a Catholic woman who has given birth to a child in legitimate wedlock, provided she has not allowed the child to be baptized outside the Catholic Church, is entitled to it. It is not a precept, but a pious and praiseworthy custom (Rituale Romanum), dating from the early Christian ages, for a mother to present herself in the Church as soon as she is able to leave her house (St. Charles Borromeo, First Council of Milan), to render thanks to God for her happy delivery, and to obtain by means of the priestly blessing the graces necessary to bring up her child in a Christian manner. The prayers indicate that this blessing is intended solely for the benefit of the mother, and hence it is not necessary that she should bring the child with her; nevertheless, in many places the pious and edifying custom prevails of specially dedicating the child to God. For, as the Mother of Christ carried her Child to the Temple to offer Him to the Eternal Father, so a Christian mother is anxious to present her offspring to God and obtain for it the blessing of the Church. This blessing, in the ordinary form, without change or omission, is to be given to the mother, even if her child was stillborn, or has died without baptism (Cong. Sac. Rit., 19 May, 1896).
The churching of women is not a strictly parochial function, yet the Congregation of Sacred Rites (21 November, 1893) decided that a parish priest, if asked to give it, must do so, and if another priest is asked to perform the rite, he may do so in any church or public oratory, provided the superior of said church or oratory be notified. It must be imparted in a church or in a place in which Mass is celebrated, as the very name "churching" is intended to suggest a pilgrimage of thanksgiving to the church, and as the rubrics indicate in the expressions: "desires to come to the church", "he conducts her into the church", she kneels before the altar", etc. Hence the Second Plenary Council of Baltimore (No. 246) prohibits the practice of churching in places in which Mass is not celebrated.
The mother, kneeling in the vestibule, or within the church, and carrying a lighted candle, awaits the priest, who, vested in surplice and white stole, sprinkles her with holy water in the form of a cross. Having recited Psalm 23, "The earth is the Lord's and the fullness thereof", he offers her the left extremity of the stole and leads her into the church, saying: "Enter thou into the temple of God, adore the Son of the Blessed Virgin Mary who has given thee fruitfulness of offspring." She advances to one of the altars and kneels before it, whilst the priest, turned towards her, recites a prayer which expresses the object of the blessing, and then, having sprinkled her again with holy water in the form of the cross, dismisses her, saying: "The peace and blessing of God Almighty, the Father, the Son, and the Holy Ghost, descend upon thee, and remain forever. Amen." - Churching of Women
Another example may be taken from the Mandatum ceremony on Holy Thursday. Our Lord set this example for us in John 13:5-10.
5 After that, he poured water into a basin and began to wash his disciples’ feet, drying them with the towel that was wrapped around him.
6 He came to Simon Peter, who said to him, “Lord, are you going to wash my feet?”
7 Jesus replied, “You do not realize now what I am doing, but later you will understand.”
8 “No,” said Peter, “you shall never wash my feet.”
Jesus answered, “Unless I wash you, you have no part with me.”
9 “Then, Lord,” Simon Peter replied, “not just my feet but my hands and my head as well!”
10 Jesus answered, “Those who have had a bath need only to wash their feet; their whole body is clean. And you are clean, though not every one of you.”
Many Religious Orders today still have a mandatum ceremony when a postulant becomes become a novice and is thus considered a canonical religious. Thus trials placed before them during the term of their postulancy is now been done away with.
Another example of this could be taken from Catholic Tradition. Yes, it is traditional, but in reality it is a religious custom, for religious to confess their sins in the sacrament of confession once a week (usually on Saturdays) that they may be spiritually clean of as much personal sin as possible in order to sanctify the Lord’s Day in a more meaningful way. This sort of “ritual practice” has very concrete meaning in the sanctification of individuals within the Church.
The only thing that can make us truly impure and unable to receive Our Lord in Holy Communion is mortal sin. Thus the weekly (at least monthly) confession our sins.
Let us make note of the words of Our Lord in regards to defilement: Matthew 15:11-20.
11 It is not what goes into the mouth that defiles a person, but what comes out of the mouth; this defiles a person.” 12 Then the disciples came and said to him, “Do you know that the Pharisees were offended when they heard this saying?” 13 He answered, “Every plant that my heavenly Father has not planted will be rooted up. 14 Let them alone; they are blind guides.[a] And if the blind lead the blind, both will fall into a pit.” 15 But Peter said to him, “Explain the parable to us.” 16 And he said, “Are you also still without understanding? 17 Do you not see that whatever goes into the mouth passes into the stomach and is expelled?[b] 18 But what comes out of the mouth proceeds from the heart, and this defiles a person. 19 For out of the heart come evil thoughts, murder, adultery, sexual immorality, theft, false witness, slander. 20 These are what defile a person. But to eat with unwashed hands does not defile anyone.”
Note: Although I am unable to find a source, it is interesting to note that in the Middle Ages, butchers were not permitted to be ordained as priests. This could be seen as a defilement and impediment to advance in Holy Orders. Again, it was not a sin to be a butcher. It simply seemed unbecoming for authorities in those days to ordain a butcher a priest. Perhaps touching dead animals was fronded?