For those who believe there was no historical Adam and Eve, how does Christianity make sense?

Wasn’t the entire point of Christ’s atonement to redeem humanity from their fall from grace, which is indeed the fault of humanity precisely because of Adam and Eve?

No, that is not the point of Christianity, much less the entire point.

Christ's sacrifice is offered to individuals, not to humanity collectively.

What Adam and Eve did has no effect on your own salvation. And whether you are personally saved has no effect on anyone else's salvation.

Sin is simply breaking any of God's laws. As 1 John 3:4 says "… sin is the transgression of the law". We were all born with a capacity to sin, even Jesus. Whether that ability to sin was created by Adam and Eve's transgression or inevitably resulted simply from the existence of law may be an interesting theological question, but it is irrelevant in terms of one's salvation or damnation.

Sin is a fact, its origin really doesn't need an explanation.

You have sinned. It really doesn't matter whether you blame your sin on Adam and Eve for what they did, on God for having created the Law, on Satan for tempting you, on simple human nature, or on some other excuse.

As a result of your sin you will experience permanent death, perpetual non-existence. It really doesn't matter why you sinned; only that you did sin.

But you, personally and individually, will be offered salvation, either now in this age, or later following the second general resurrection. You can accept it, or reject it; the choice is yours alone.

You asked:

How does this make sense from a theological perspective? How can the theologically "progressive" Christian explain the origin of sin, humanity’s state of sin, and the purpose of Christ’s atonement without resorting to Adam and Eve?

Well... the proper answer is "it doesn't" and "they can't". Not, anyway, if they are to seriously consider the problem. I could point you to this answer to a different question, and also the articles here, here and here for a deeper explanation of why this problem exists, but it seems you are already familiar with the issue.

So... what? Well, the "solution" is to ignore the problem. Some do so out of ignorance, not realizing the extent of the inherent contradiction in believing in both Christianity and Evolutionism (and its necessarily attendant Uniformitarianism). Others perhaps do so willfully; humans are fairly skilled at doublethink. Basically, tell yourself that it doesn't matter, that it doesn't apply to your life right now. And, to be fair, there is some truth in this; I'm not arguing that belief in YEC is necessary to be saved (further reading).

I could also point out that this wouldn't be the only confusing thing about Christianity that (many) Christians accept on faith (the Trinity, anyone?). I could also point out that a child-like faith is seen in some senses as a good thing. The trouble here, however, is that the N/U/E triumvirate is inherently antithetical to Christianity. If one fails to reject it, one has allowed a seed to be planted with the potential to grow and undermine one's faith. Moreover, there is no need to reject a literal Adam and Eve; if one excludes the Naturalist dogma that there is no God, there is actually much scientific support for Biblical Creation. The "theistic evolutionist" denies a part of God's Word, leaving the door open to denying other parts, and essentially has a faith resting upon hollow foundations. The YEC, on the other hand, has a faith firmly planted on the bedrock of revealed truth.

From a personal point of view, it is because the exact interpretation of what the Adam and Eve story really represents has no influence on my day to day life. I can see that interpretations that posit that Adam and Eve were two people exist, and those that posit that Adam and Eve were a community of (proto) humans exist, and those that posit that is it an allegory of the development of the human condition exist. None of these actually differ in how I should live my life, therefore it is not required for me to decide with any certainty which explanation I hold to be most accurate.

How can the theologically “progressive” Christian explain the origin of sin, humanity’s state of sin, and the purpose of Christ’s atonement without resorting to Adam and Eve?

With big confidence intervals. I know that explanations exist for all these things under the different interpretations, I do not have good reason to accept of reject any and none result in different answers to the immediate questions of "what should I do in situation X". Given this level of uncertainty and the lack of importance of knowing for certain the correct answer a big confidence interval works for me.

Do note that this is not a case of ignoring the consequences of different interpretations, but of understanding that uncertainty exists. My priority is to determine which interpretations have an influence on my decisions, and concentrating my efforts on those. While the different interpretations of Adam and Eve are very interesting, in particular in respect to the rapidly expanding knowledge of human genetic diversity, both in modern humans and archaeological remains, it does not influence my day to day life so I am content to file such interpretations under "interesting but do not need a definitive answer today".

OP: "How can the theologically “progressive” Christian explain the origin of sin, humanity’s state of sin, and the purpose of Christ’s atonement without resorting to Adam and Eve?"

Adam and Eve, whether allegory or factually accurate, is a revelation of man's state from our three-part essence to our two-part essence and, if a born-again Christian, back to our three-part essence.

Originally, we were body, soul, and spirit. By sinning, our spirit died. Flesh begets flesh. Spirit begets spirit, but man can't do that; it comes from God.

The contrast between Christianity and all other religions is the question whether you have a "light", a "spirit", an internal eternal "piece". Christianity says no, unless you are born again (spirit). Other religions say yes you do. The word "namaste" is a manifestation of this. It means I salute the light in you with the assumption that all people have said light.

So, the origin of sin and humanity's state of sin and its solution is explained whether Adam and Eve actually existed or not. Somewhere in the way back someone disobeyed, died spiritually, and the best that happened until Christ Jesus was to physically procreate.

Hope that helps.

PS You can find these various themes in the story of Adam and Eve. For example, God said on the day you sin you die. But Adam and Eve continued to live another 900 or so years. They died spiritually on that day of the "apple eating", but continued physically.

For those who believe there was no historical Adam and Eve, how does Christianity make sense?

How can Christianity make sense without a literal Adam and Eve?

In a sense, one can not, at least in the sense that for the average Christian to understand the various aspects of this question, one has to believe that there at least had to be a first man and a first woman. It matters little if we call them Adam and Eve. The paramount belief to hold on to is that there was in the history of humanity, a first man and a first woman, at the beginning of mankind, and that our first parents sinned against God and as a result passed on original sin to all the descendants of humanity.

I enjoy reminding others of Galileo’s now famous statement:

”The Bible shows the way to go to heaven, not the way the heavens go”, was made by Galileo Galilei (1564- 1642 in his open letter to the Dowager Grand Duchess.

As I just stated, it matters little that we call our first parents Adam and Eve. The thing here to retain is that human race had a first father and mother to make sense of God’s salvation for humanity.

What Does Adam Mean?

If you're looking for a name with strong historical significance, you can't go wrong with Adam.

A well-known Hebrew name, Adam means "son of the red Earth." Its meaning comes from the Hebrew word "adamah" meaning "earth," from which Adam is said to be formed. The name also refers to the reddish color associated with human skin. Adam was, of course, pivotal to the Old Testament, being the first man God ever created.

Eve

Meaning & History

From the Hebrew name חַוָּה (Chawwah), which was derived from the Hebrew word חָוָה (chawah) meaning "to breathe" or the related word חָיָה (chayah) meaning "to live". According to the Old Testament Book of Genesis, Eve and Adam were the first humans. God created her from one of Adam's ribs to be his companion. At the urging of a serpent she ate the forbidden fruit and shared some with Adam, causing their expulsion from the Garden of Eden.

For those who believe In real and historical Adam and Eve, as told in the book of Genesis, the whole idea of a first man and a first woman along with their first sin against God and the consequences that unfolded are clearly understood and believed by most of these Christians.

However, for those Christians who do not hold to the literal sense as explained in the Book of Genesis, is to remember that our first parents committed the first sin, the original sin, that damaged our human nature and left each of us with an inclination towards sin in our very nature.

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 "polygenism", 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

Thus without the sin of Adam, our first parent, there is no original sin or an accurate explication of why there is sin in the world.