Was Dr. Rogers Roman Catholic or Orthodox?

PART ONE THE PROFESSION OF FAITH
SECTION TWO THE PROFESSION OF THE (ROMAN CATHOLIC) CHRISTIAN FAITH

416 By his sin Adam, as the first man, lost the original holiness and justice he had received from God, not only for himself but for all human beings.
417 Adam and Eve transmitted to their descendants human nature wounded by their own first sin and hence deprived of original holiness and justice; this deprivation is called "original sin".
418 As a result of original sin, human nature is weakened in its powers, subject to ignorance, suffering and the domination of death, and inclined to sin (this inclination is called "concupiscence").

406 The Church's teaching on the transmission of original sin was articulated more precisely in the fifth century, especially under the impulse of St. Augustine's reflections against Pelagianism, and in the sixteenth century, in opposition to the Protestant Reformation. Pelagius held that man could, by the natural power of free will and without the necessary help of God's grace, lead a morally good life; he thus reduced the influence of Adam's fault to bad example. The first Protestant reformers, on the contrary, taught that original sin has radically perverted man and destroyed his freedom; they identified the sin inherited by each man with the tendency to evil (concupiscentia), which would be insurmountable. The Church pronounced on the meaning of the data of Revelation on original sin especially at the second Council of Orange (529) and at the Council of Trent (1546).

The 2000 Baptist Faith and Mission
III Man
Through the temptation of Satan man transgressed the command of God, and fell from his original innocence whereby his posterity inherit a nature and an environment inclined toward sin. Therefore, as soon as they are capable of moral action, they become transgressors and are under condemnation. Only the grace of God can bring man into His holy fellowship and enable man to fulfill the creative purpose of God.

Westminister Shorter Catechism
Q. 18. Wherein consists the sinfulness of that estate whereinto man fell?
A. The sinfulness of that estate whereinto man fell, consists in the guilt of Adam’s first sin, the want of original righteousness, and the corruption of his whole nature, which is commonly called original sin; together with all actual transgressions which proceed from it.

Q. 19. What is the misery of that estate whereinto man fell?
A. All mankind by their fall lost communion with God, are under his wrath and curse, and so made liable to all the miseries of this life, to death itself, and to the pains of hell forever.

Since Adrian Rogers preached against Reformed Theology (Westminister Catechism) then no other conclusion can be formed than that he was closer to Roman Catholicism than Orthodoxy.