How do Christians who believe in evolution understand Original Sin? As I understand, many Christians nowadays accept evolution. There are such Christians in most major denominations and inside these denominations exist different traditions and groups of believers, so I understand that there may be different theories in those traditions for how to combine evolution with Christianity. Those theories may broadly be called Theistic Evolution. There may also be individual ideas which are not part of the teaching of a specific denomination, but are plausible theories in which some of the Christians believe, which I am also ready to explore.
Do those who are Christians and accept evolution at the same time, think that there was no Adam and Eve? If so, does this mean that there was no original sin?
What are the main modern theories how to understand Original Sin (The idea that the humankind changed after the first sin and that people as children of Adam and Eve bear the consequences of this first sin) when believing in evolution at the same time?
How do Christians who believe in evolution understand Original Sin?
Before getting into the crux of this question, it should simply be noted that not all Christian denominations believe in Original Sin or evolution for that matter.
If we as Christians are to believe in evolution and original sin, there has to be a logical and theological manner to join these two thoughts within a philosophical logical thought.
If the creationist holds to a literal interpretation of creation and with it, the belief that Adam was responsible for our original sin; then those who hold to the theory of evolution and Original Sin must hold that our first parents of the human race also committed the original sin.
In order that original sin and evolution be reconciled, it would be necessary that at a certain time in evolution, God infused into a certain natural creature an immortal soul and the gift of intelligence and knowledge of God. This being would be our first parent: Adam. This is what evolutionists accept in order to make original sin understood within a Christian belief system.
For example, Pope Pius XII's teaching in Catholicism can be summarized as follows:


The question of the origin of man's body from pre-existing and living matter is a legitimate matter of inquiry for natural science. Catholics are free to form their own opinions, but they should do so cautiously; they should not confuse fact with conjecture, and they should respect the Church's right to define matters touching on Revelation.

Catholics must believe, however, that humans have souls created immediately by God. Since the soul is a spiritual substance it is not brought into being through transformation of matter, but directly by God, whence the special uniqueness of each person.

All men have descended from an individual, Adam, who has transmitted original sin to all mankind. Catholics may not, therefore, believe in &quot;polygenism&quot;, the scientific hypothesis that mankind descended from a group of original humans (that there were many Adams and Eves). - Evolution and the Catholic Church



St. Paul’s words can not be altered and will always remain a strong testimony of Divine truth:

11Not only that, but we also rejoice in God through our Lord Jesus Christ, through whom we have now received reconciliation. 12Therefore, just as sin entered the world through one man, and death through sin, so also death was passed on to all men, because all sinned. 13For sin was in the world before the law was given; but sin is not taken into account when there is no law. - Romans 5:11-13

Evolution contradicts a literalistic interpretation of Genesis; however, according to Catholicism and most contemporary Protestant denominations, biblical literalism in the creation account is not mandatory. Christians have considered allegorical interpretations of Genesis since long before the development of Darwin's theory of evolution, or Hutton's principle of uniformitarianism. A notable example is St. Augustine (4th century), who, on theological grounds, argued that everything in the universe was created by God in the same instant, and not in six days as a plain reading of Genesis would require.
Modern Catholicism points to a unique special creation applies to humans and not other species:

The position of the Roman Catholic Church on the theory of evolution has changed over the last two centuries from a large period of no official mention, to a statement of neutrality in the early-1950s, to limited guarded acceptance in recent years, rejecting the materialistic and reductionist philosophies behind it, and insisting that the human soul was immediately infused by God, and the reality of a single human ancestor (commonly called monogenism) for all of mankind. The Church does not argue with scientists on matters such as the age of the earth and the authenticity of the fossil record, seeing such matters as outside its area of expertise. Papal pronouncements, along with commentaries by cardinals, indicate that the Church is aware of the general findings of scientists on the gradual appearance of life. Indeed, Belgian priest Georges Lemaître, astronomer and physics professor at the Catholic University of Louvain, was the first to propose the theory of expansion of the universe, often incorrectly credited to Edwin Hubble. In the 1950 encyclical Humani generis, Pope Pius XII confirmed that there is no intrinsic conflict between Christianity and the theory of evolution, provided that Christians believe that the individual soul is a direct creation by God and not the product of purely material forces. Today, many members of the Church support theistic evolution, also known as evolutionary creation. Under Cardinal Joseph Ratzinger, the International Theological Commission published a paper accepting the big bang of 15 billion years ago and the evolution of all life including humans from the microorganisms that formed approximately 4 billion years ago. The Vatican has no official teaching on this matter except for the special creation of the human soul. The Pontifical Biblical Commission issued a decree ratified by Pope Pius X on June 30, 1909, stating that special creation applies to humans and not other species. - Acceptance of evolution by religious groups

Without the sin of Adam, our first parent there is no
original sin.