Lust, gluttony, greed, sloth, wrath, envy, and pride. One can see that each of these can be very bad, if taken to an extreme. Most people give some vitality to each of these in their lives--nobody is perfect. What is the Objectivist stance on the SDS?
There is a substantial article on "Seven deadly sins" on Wikipedia. The opening paragraph explains:
The seven deadly sins, also known as the capital vices or cardinal sins, is a classification of vices (part of Christian ethics) that has been used since early Christian times to educate and instruct Christians concerning fallen humanity's tendency to sin. In the currently recognized version, the sins are usually given as wrath, greed, sloth, pride, lust, envy, and gluttony. Each is a form of Idolatry-of-Self....
Secular altruist-collectivists, too, have often adopted the term "sin" in their own moral exhortations. See, for example, the story in Anthem, in which Chapter 1 begins:
IT IS A SIN TO WRITE THIS. It is a sin to think words no others think and to put them down upon a paper no others are to see. It is base and evil. It is as if we [the narrator, who has not yet learned the long-forgotten word "I"] were speaking alone to no ears but our own. And we know well that there is no transgression blacker than to do or think alone. We have broken the laws. The laws say that men may not write unless the Council of Vocations bid them so. May we be forgiven!
But there are no "sins" in Objectivist ethics. Objectivist ethics does not use that term in regard to any of its ethical principles. There are virtues and vices in Objectivism, values and disvalues, ideals and evils -- but no sins. Objectivism identifies three cardinal values as essential for man's life qua man: reason, purpose, self-esteem. Objectivism identifies seven essential virtues as the actions by which to gain and/or keep the cardinal values: rationality (the primary virtue), with corollary virtues of honesty, independence, integrity, productiveness, pride, and justice. Objectivism identifies these values and virtues not as commandments from another "dimension" or as absolute social conventions, but as requirements imposed by reality for man's life qua man. The idea of "sin" basically refers to violating the ethical standards of others (including religious standards, insofar as they are accepted in a society). "Sin," as a reference to social conventions or mystical commandments, is alien to Objectivist ethics.
And why are the seven alleged "sins" regarded as "deadly"? Deadly how or why, and for whom? Objectivism denies that they are necessarily deadly to man's life qua man (man's life in the secular, earthly world). Does "deadly" perhaps mean deadly to some alleged disembodied "spiritual life" after bodily death? Does it mean potentially deadly even on earth, if an alleged all-powerful promulgator of moral commandments decides to strike down transgressors? I do not know enough about conventional moral standards to say why conventional sins would be considered deadly. It would actually be a step forward in the history of philosophy if someone were to attempt to defend the seven "sins" (as being sins) on the basis of the requirements of man's life qua man as the fundamental standard of value.
Objectivism strongly criticizes conventional morality as anti-life. It is adherence to conventional (altruistic) moral standards that leads to bodily, earthly death, not the violation of those standards. But the purveyors of conventional morality already know this, and they count on it. Ayn Rand offers one such concretization in the character of Ellsworth Toohey in The Fountainhead. In a private speech (an extended confession) to Peter Keating, Toohey (a secular altruist-collectivist) proclaims (p. 77 in FNI, wherein "The Soul of a Collectivist" spans pp. 76-83):
I shall rule....
Objectivism rejects the whole idea of "sin" and its conventional moral context. Early in Galt's speech in Atlas Shrugged, John Galt states:
For centuries, the battle of morality was fought between those who claimed that your life belongs to God and those who claimed that it belongs to your neighbors—between those who preached that the good is self-sacrifice for the sake of ghosts in heaven and those who preached that the good is self-sacrifice for the sake of incompetents on earth. And no one came to say that your life belongs to you and that the good is to live it.
The question asks: "What is the Objectivist stance on the SDS?" Objectivism does not present "stances." Ayn Rand challenged the term "stance" in CUI, Chap. 20, "The New Fascism: Rule by Consensus" (p. 210):
"Pragmatic"—not "idealistic"—is their [liberals'] favorite adjective when they are called upon to justify their "stance," as they call it, not "stand."
An Objectivist stand on Original Sin can be found in Galt's speech. An Objectivist view of the seven "sins" can be discerned by studying the positive elements of the Objectivist ethics (each cardinal value and essential virtue has a corresponding entry in The Ayn Rand Lexicon), then comparing them to the seven "sins" one-by-one. Here is a rough list of comparisons pertaining roughly to the same or similar issues:
One will not be able to learn much about Objectivism or a proper Objectivist rejection of conventional moral views without studying Objectivist materials directly and in their proper context.
Update: Pragmatic Approach
My initial Answer (above) describes the assault on integrity and the resulting guilt infection that the SDS perspective fosters among people who want to live (on earth). The conventional moral code, by its nature, cannot be practiced consistently in daily living. But rather than challenge the code, the victims accept the loss of integrity and the resulting sense of guilt over their alleged moral "unworthiness."
There is, however, another distinctively American response to the impracticality of conventional moral standards: one can accept the loss of integrity and then deny that integrity is possible to man on earth at all. One can deny that it is ever practical to live by principles (consistently) in any form.
The present Question is steeped in the language of pragmatism (underlined):
One can see that each of these ["sins"] can be very bad, if taken to an extreme. Most people give some vitality to each of these in their lives--nobody is perfect. What is the Objectivist stance...?
In the comments, the questioner reiterates the pragmatic perspective:
If you are guilty of an extreme of any of these [seven] sins--philosophically relevant or not--you shall mainly harm yourself. It can [also] affect others.
The implication is that a "less extreme" practice of the "sins" does not harm oneself, and may indeed be highly beneficial. If "harm to oneself" is the basis for classifying an action as "sinful," then the seven "sins" would have to be considered sinful only if performed consistently, i.e., taken to the extreme. That is not the typical religious view of the seven "sins," however. In the typical religious perspective, the seven sins are sinful through and through, in any degree, whether taken to an "extreme" (i.e., performed fully consistently) or not. Religions do not say that it is morally "ok" to be partly sinful, as long as one isn't "extreme" about it. Religions seek to undercut the practice of the "sins" to whatever degree is possible, and gladly accept partial aversion to the "sins" in lieu of a totally guiltless lack of any aversion to them at all, since even a partial breach of integrity constitutes the loss of integrity. Pragmatists, in turn, renounce the whole field of principles, abandoning it to the religionists by default. Pragmatists view the "problem of morality" as attempting to live by principles at all. Neither bad principles nor overt abandonment of principles can work very well in the long run, since man needs long-range principled guidance in order to live. Objectivism rejects both conventional moral standards and the pragmatic attempt to ignore principles, offering man a fundamentally new moral code built consistently on the standard of man's life qua man. That is Objectivism's stand. In the words of John Galt in his climactic speech in Atlas Shrugged:
The fence you have been straddling for two hours—while hearing my words and seeking to escape them—is the coward's formula contained in the sentence: 'But we don't have to go to extremes!' The extreme you have always struggled to avoid is the recognition that reality is final, that A is A and that the truth is true. A moral code impossible to practice, a code that demands imperfection or death, has taught you to dissolve all ideas in fog, to permit no firm definitions, to regard any concept as approximate and any rule of conduct as elastic, to hedge on any principle, to compromise on any value, to take the middle of any road. By extorting your acceptance of supernatural absolutes, it has forced you to reject the absolute of nature. By making moral judgments impossible, it has made you incapable of rational judgment. A code that forbids you to cast the first stone, has forbidden you to admit the identity of stones and to know when or if you're being stoned.
(From FNI, pp. 193-194 in the Signet paperback edition in which Galt's speech spans pp. 130-216.)
For further insight on the Objectivist view of principles, pragmatism, compromise, and integrity, refer to those topics in The Ayn Rand Lexicon.