I'm interested in both Catholic and Orthodox answers to how Adam's sin was passed on.
Catholic doctrines around the blessed Mary, seem to imply genetic transfer of sin. That is you get it from you parents. It appears to me as a non "Cathodox" Christian, that Catholics believe that blessed Mary had to be sinless so as not to pass sin onto Christ?
I have always held to "federal" view of Adam's sin from Rom 5:12. Adam as our human representative, chose sin and that impacted us, as we were represented by him and impacted by his choice. The effects of Adamic sin doesn't come from our parents but from Adam's headship of humanity. However Christ, being the 2nd person of the trinity, was not under Adam's headship, so Adam's sins effect was not transmitted to him.
Is standard Catholic position that sin is passed directly from our parents?
Christ is like us in every way except for sin.
Federal Headship, as suggested here, makes man the actual thing we call sin, which of course we are not. As I have noted before, this creates a pernicious god. It stems from the desire to remove Mary from God's plan for our redemption. Christ must have an earthly mother to satisfy prophecy; the last I heard this requires a woman, Mary. With the concept of "Federal Headship" Mary can bear a man who is sin yet as the Calvinist claim is the Personification of the Word, a contradiction. The idea of sin hanging on a cross as reparations for the sins of man and the concept of the Personification of God's Breath within Christ as Theandric is an absurdity of types. The reformer then must remove Mary from God's plan to lead us into the wilderness of heresy and hell, because of their objection that Mary (a human) becomes God's instrument of our salvation.
This Calvinist error rests in a simple denial of sin and by extension the heresy of "once saved always saved". Sin, however, is a voluntary immoral act. When this simple concept is acknowledged then we find that men can 'work' in concert with God's will for Sanctification. God's justice is a punishment, a physical death and the death of the soul of all those born of Adam. He does not re-make His creation into sin itself; rather he deprives us of His justice and mercy.
Adam having fee will was one with God (oneness such as John 6:57 and John 17:21-22). Both Adam and Eve were made in the image and likeness of God, and they were one with God, i.e. spoke face to face with God. Whether Eden was a physical place on earth or a state of being is not important here. In either case, "God saw all the things that he had made, and they were very good."
What God had made was good. Sin does not re-make man evil. Rather it is the freewill of men, voluntarily acting in opposition to 'good'. As such we view original sin as the privation of sanctification, an abiding in God and God abiding in us. As I've written before Johann Eck exposes the converse for the heresy it is.
Original Sin is that men are born without the fear of God and without trust in God, is to be entirely rejected, since it is manifest to every Christian that to be without the fear of God and without trust in God is rather the actual guilt of an adult than the offense of a recently-born infant, which does not possess as yet the full use of reason, as the Lord says "Your children which had no knowledge between good and evil," Deut 1:39. (Johann Eck, The Confutatio Pontificia, 1530)
More succinctly we see that guilt requires a voluntary act and that sin is an evil act,
“… sin is nothing else than a bad human act. Now that an act is a human act is due to its being voluntary, whether it be voluntary, as being elicited by the will, e.g. to will or to choose, or as being commanded by the will, e.g. the exterior actions of speech or operation. Again, a human act is evil through lacking conformity with its due measure: and conformity of measure in a thing depends on a rule, from which if that thing depart, it is incommensurate. Now there are two rules of the human will: one is proximate and homogeneous, viz. the human reason; the other is the first rule, viz. the eternal law, which is God's reason, so to speak. See Contra Faustum . xxii, 27
CHURCH FATHERS: Contra Faustum, Book XXII (Augustine), St. Thomas Aquinas, Summa Theologica, I, II, 71,6
Key to the point is punishment or merit for any act relies on that act being voluntary, i.e. "Now both justice and injustice, to be acts at all, must be voluntary; otherwise, there can be no just rewards or punishments; which no man in his senses will assert. (St. Augustine, Contra Faustum . xxii, 78) Adam's sin was a voluntary act for which God's justice brought death, physical and spiritual, i.e. the life leaves the physical body, and life (sanctification) leaves the soul. It is God's plan in the New Covenant through the first graces of Baptism that sanctification re-instills, as it were, drop by drop or bite by bite, the 'fullness of salvific grace' in man. In Baptism the punishment for the first sin of Adam is removed, there being no guilt in the individual because the sin committed by Adam was not a voluntary act of the individual. We can see through the lens of Baptism how the nature of original sin stains all of mankind. St. Thomas explains it best:
"An individual can be considered either as an individual or as part of a whole, a member of a society . . . . Considered in the second way an act can be his although he has not done it himself, nor has it been done by his free will but by the rest of the society or by its head, the nation being considered as doing what the prince does. For a society is considered as a single man of whom the individuals are the different members (St. Paul, 1 Corinthians 12). Thus the multitude of men who receive their human nature from Adam is to be considered as a single community or rather as a single body . . . . If the man, whose privation of original justice is due to Adam, is considered as a private person, this privation is not his 'fault', for a fault is essentially voluntary. If, however, we consider him as a member of the family of Adam, as if all men were only one man, then his privation partakes of the nature of sin on account of its voluntary origin, which is the actual sin of Adam" (De Malo, 4, 1).
We can therefore conclude original sin is not 'transmitted', as it were, like a virus from male or female (one or both gender) to their offspring, both punishment and guilt handed down from generation to generation. Rather it is a condition of being a member of the human species after the fall of Adam. We use the term inherited only to explain that all of mankind after Adam's fall receives the effects of God's justice without the guilt whereby we receive from Adam a privation of sanctification. So, in this way, a child born, even from a process of cloning, is subject to original sin. Conversely, a child born whose Father is the Spirit of God and whose mother is a New Eve, one without the stain of sanctification's privation is a New Adam, a human like Adam in perfect union with God, i.e. Christ.
The concept of Federal Headship confounds God's plan for the salvation of men: it makes your god pernicious and sadistic putting Him opposition to His own creation.