Your question is probing the limits of existential and absurdist thinking regarding morality. It is a common trope among theologians that deviation from absolutist transcendental truth is tantamount to an endorsement of anarchy and evil. Absurdism might be seen as an atheistic form of existentialism that doesn't abandon truth and morality, but rather wrests it firmly away from the supernatural and places the burden on the shoulder of the thinker. As an absurdist who moved beyond Sartre, I must plead that this is not the same as the implication in your question that an absurdist would accept psycopathy and lawlessness as acceptable.
Camus and absurdism don't endorse complete relativity of fact and morality, but merely push back very firmly on the notion that society and supernatural narratives are reliable. This is clearly evident in The Plague, where the protaganist, Dr. Rieux, a man of science and ethical conduct, examines meaning and behavior amid an epidemic in North Africa. Ultimately, one can draw a firm line between absurdism which rejects gods and mob mentality from nihilism where anything goes. We absurdists are not amoral nor do we reject psychological altruism out of hand.
Existentialism, Absurdism, Subjectivism, and Relativism
My understanding of Camus is that he thinks you should find your subjective interests and run with them, but what would he say to say to a clinical psychopath born without a conscience who says he finds meaning in violating the rights of others?
While Camus rejects the supernatural, absurdism is more subjectivism than relativism, though there is some overlap. The difference between the two amounts to how one looks at the foundation of morality and ethics. Subjectivist thinking in ethics would essentially argue that people disagree on morality and for different reasons, whereas relativistic thinking would be closer to adhering to the idea that there is no right or wrong. Camus and absurdism fall under the former because of his belief in morality and the limits of human ability.
From WP: Albert Camus:
Camus poses a crucial question: Is it possible for humans to act in an ethical and meaningful manner, in a silent universe? According to him the answer is yes, as the experience and awareness of the Absurd creates the moral values and also sets the limits of our actions.
Absurdism is the doctrine that meaning and morality in life come from a recognition of the inherent meaninglessness of life to begin with. Whereas those who tout theological bases of morality essentially appeal to morality by fiat (God is good, and his teachings define good), an absurdist must content with the idea that life starts with an inherently meaningless state and construct meaning particularly making sense of so much absurdity. (Goodness is my personal project, and I must start by recognizing that I cannot rely on God, gods, or society to define good.) Sometimes Camus is lumped in with existentialism for this reason.
Morality, Ethics, and Good and Evil
Existentialism and absurdism don't advocate that any claimed morality is morality (one of the limits of being is that one cannot declare oneself a god), but rather that it must be consistent with the intersectionality of the temperament of the individual and facts. Absurdism is also not factually relativistic. Indeed, the main protagonist in The Plague, Dr. Rieux is a medical doctor and a man of science, and one who recognizes evil in the world. See the PhilSE post on Rieux. From page 125 Rieux says:
What's true of all the evils in the world is true of plague as well. It helps men to rise above themselves. All the same, when you see the misery it brings, you'd need to be a madman, or a coward, or stone blind, to give in tamely to the plague.
So, anyone who uses the existence of psychopathy coupled with some absolutist moral relativism is crafting a strawman against absurdism. Camus didn't advocate chaos or endorse the abandonment of value, but merely railed against (like the existentialists) borrowing an inauthentic morality from society, particularly religion. This is the morality that is a false consciousness, one that isn't often consistent when it preaches love but practices war and terror, one that promises gifts from the supernatural, but one that is doctrinaire. Rieux goes on to say:
Paneloux (the town priest) is a man of learning, a scholar. He hasn't come in contact with death; that's why he can speak with such assurance of the truth.
And on page 127:
I have no idea what's awaiting me, or what will happen when all this ends. For the moment I know this; there are sick people and they need curing... What's wanted now is to make them well. I defend them as best I can, that's all.
Absurdists simply don't abandon human decency wholesale because they reject absolutist transcendental morality.
Truth in Pretense
Lastly, a quick response on finding meaning in pretense. Yes, it is possible to find meaning in pretense. Some people devote their lives to and look for wisdom in fictional narratives. But among philosophers, epistemological thinking generally and broadly holds that truth and/or Truth must be justfied, true, and believed. For existentialism and absurdism, this is particularly true because the credo is to pursue what is authentic. Thus, living a life devoted to a religious doctrine that one does not actually believe in is a form of fear or cowardice. It's precisely squaring off against that fear nihilism that is the source of existential terror. Roughly speaking, the main difference between an existentialist and an absurdist is that an existentialist ultimately appeals to a philosophy where one connects with a greater meaning which might even be theological (existentialism doesn't endorse athiesm), whereas an absurdist goes down the athiestic road with certainty.