Existentialists can be hopeful and not; they can be Christians or criminals. They can be ministers and murderers.
Walter Kaufmann claims existentialism is by nature a "revolt" against traditional philosophy, not "reducible to any set of tenets," instead relying on a "timeless sensibility" only recently evolved into a "sustained protest." He dates the protest to the earlier generations of monastic theologians, claiming: "First, religion has always been existential: It has always been preoccupied with suffering, death, and dread, with care, guilt, and despair."
In broad terms, an existentialist asserts that an individual is determined from within, not from outside theories. On the human and literary level what makes existentialists and their heroes homogeneous is their "perfervid individualism." But their "refusal to belong to any school of thought, the[ir] repudiation of the adequacy of any body of beliefs whatsoever, and especially systems," has made them easy targets for critics who see their rejections as nihilistic and heretical.
Existential heroes are the opposite of essentialist ones: remember, existence precedes essence (actus essendi). Essence refers to what man is (his nature); existence denotes that "he is." Thus, "I am a man" is first part existence ("I am") and second part essence ("a man.") This is in opposition to traditional Platonic essentialism (think "Parable of the Cave"), which embraces man's essence prior to his existence, that man has an eternal, unchangeable human nature. St. Thomas refutes this by affirming that man's existence cannot coincide with essence; otherwise conjoined man's essence would be to exist and never die.
Andy remains a perfervid individual throughout the novella. He enjoys the company of others, but he remains outside the system. He doesn't even partake in the bottle of suds on top of the roof; instead, he smiles as he and the men relish their freedom.
So Andy learns that he cannot align his freedom with traditional systems; he tries this by putting his faith in the library he helped build. This gives him intellectual freedom, but he was still a prisoner in a system.
Andy's key to freedom is through books--not the books in the library (external system), but through the Warden's books (internal): his ledger and Bible. In fact, he uses the Bible to hide his rock hammer. Andy is reluctant to align his freedom with criminal activity. In this way, he becomes like Sartre's existential hero, Orestes in "The Flies," who must murder his mother to become free. Andy is also like the Underground Man Dostoevsky wrote about. So says eNotes:
[The Underground Man] is a man of free will, and he will do almost anything, even contradict himself, to prove it. It is because he uses his free will that he feels alive. This also, more than anything else in his life, makes him proud. He might commit some of the most vile actions, but at least he has expressed his emotions, his personality, and his individualism in doing them.
The problem with seeing Andy Dufresne as an existential hero goes directly to both the core of the meaning of the novella and the essence of what it means to be an existential hero. And that is the concept of hope. Hope is not part of an existentialist's world. I know this sounds bleak, but understand, to an existentialist, hope is bleak. A true existentialist accepts and experiences his life as it comes to him, without a belief in a better future or, indeed, an afterlife.
Andy is not only all about bettering his present circumstances, he spends all of his time in prison trying to get out. He dreams of a blue beach with white sand at a place called Zihuatanejo. Andy Dufresne is motivated by and fixated on a vision of a better tomorrow. No existential hero would ever do such a thing.
In many respects, Andy can be seen as an existential hero. If we understand existentialism to be that human beings exist without the totalizing presence of transcendence, there is much in Andy's background to indicate that he is of the existentialist mode. He understands that there is little in the way of morality or pure justice that guides human beings and their actions. The system of jurisprudence found him guilty, even though he is purely innocent ("Only innocent man in Shawshank.") The man who actually committed the crime is not punished, and even when Andy suggests the need of a new trial, he is silenced. Warden Norton, who invokes the presence of divinity, is more corrupt than most of the criminals in Shawshank. Andy realizes that he is only possesses his freedom, and this allows him to understand what he has to do in order to survive through the challenging conditions of Shawshank. He is an individual who only has freedom and hope, human constructs in an inhuman world. In this paradigm, Andy can be seen as an existential hero.