TL;DR: Stevenson didn’t intend to put an anti-science agenda into Strange Case of Dr Jekyll and Mr Hyde, and I don’t see how to make a convincing case for finding it there.
The question is ambiguous as written: I am not sure whether you mean to ask whether it is possible to interpret the novel as anti-science, or whether Stevenson intended this. The word ‘agenda’ suggests intention, so I’ll treat that first.
Stevenson wrote that his initial theme was:
that strong sense of man’s double being which must at times come in upon and overwhelm the mind of every thinking creature
Robert Louis Stevenson (1888). ‘A Chapter on Dreams’. Scribner’s Magazine, January 1888. Collected in Across the Plains, 1892.
His biographer gave a substantially similar account:
A subject much in his thoughts at this time was the duality of man’s nature and the alternation of good and evil; and he was for a long while casting about for a story to embody this central idea.
Graham Balfour (1901), The Life of Robert Louis Stevenson, vol. 2, p. 12.
The detail of the powders and the transformation came to Stevenson in a dream:
For two days I went about racking my brains for a plot of any sort; and on the second night I dreamed the scene at the window, and a scene afterward split in two, in which Hyde, pursued for some crime, took the powder and underwent the change in the presence of his pursuers.
In the small hours of one morning, I was awakened by cries of horror from Louis. Thinking he had a nightmare, I awakened him. He said angrily: “Why did you wake me? I was dreaming a fine bogey tale.” I had awakened him at the first transformation scene.
Fanny Stevenson, quoted in Balfour (1901), p. 13
Stevenson quickly wrote a first draft of the story, but his wife pointed out that he had omitted the intended theme:
Mrs. Stevenson, according to the custom then in force, wrote her detailed criticism of the story as it then stood, pointing out her chief objection—that it was really an allegory, whereas he had treated it purely as if it were a story. In the first draft Jekyll’s nature was bad all through, and the Hyde change was worked only for the sake of a disguise.
Balfour (1901), p. 13
According to Balfour’s account, Stevenson “realised that he had taken the wrong point of view” and immediately burned the draft manuscript and embarked on a completely new version which became the published text.
So Stevenson’s intended theme was our “double being” and
the business of the powders, which so many have censured, is, I am relieved to say, not mine at all, but the Brownies’.
(The ‘Brownies’ being the imaginary spirits “who do one-half my work for me while I am fast asleep” in Stevenson’s fanciful description of his dreams.)
Of course, just because an author intended a work to express one theme, does not prevent readers from finding other themes there. And the idea of “double being” is vague and could point at multiple targets.
Nonetheless I think it worth pointing out that although the question raises the idea that Strange Case of Dr Jekyll and Mr Hyde might be anti-science, nowhere does it actually make anything amounting to an argument. And I think that if you tried to make such an argument then you’d find there’s really nothing in the text to support it. Indeed, there’s hardly any mention of science at all: Jekyll is a scientist, yes, but we learn almost nothing about his researches, not even his field of study. There is a bare mention of Jekyll’s “scientific heresies” but no explanation of what they are; and we learn that Lanyon and Jekyll have “differed at times on scientific questions” but not what those questions were. There’s no scientific content in the novel for it to be in opposition to, no target for it to attack.
We might try to argue that the book is a warning that science reveals things that we were not meant to know. But a careful look at “Henry Jekyll’s full statement of the case” shows that it is quite otherwise. Jekyll always knew that he had a double nature, even before he began his scientific research:
It was on the moral side, and in my own person, that I learned to recognise the thorough and primitive duality of man; I saw that, of the two natures that contended in the field of my consciousness, even if I could rightly be said to be either, it was only because I was radically both; and from an early date, even before the course of my scientific discoveries had begun to suggest the most naked possibility of such a miracle, I had learned to dwell with pleasure, as a beloved daydream, on the thought of the separation of these elements.
Robert Louis Stevenson (1886), Strange case of Dr Jekyll and Mr Hyde, London: Longmans, p. 108.
We might argue that his scientific discoveries had created the evil Hyde persona. But again, it is quite the opposite. Jekyll writes that he was always disposed to “pleasures” that required “profound duplicity” to conceal:
And indeed the worst of my faults was a certain impatient gaiety of disposition, such as has made the happiness of many, but such as I found it hard to reconcile with my imperious desire to carry my head high, and wear a more than commonly grave countenance before the public. Hence it came about that I concealed my pleasures; and that when I reached years of reflection, and began to look round me and take stock of my progress and position in the world, I stood already committed to a profound duplicity of life.
Stevenson (1886), p. 106.
(The novel is deliberately vague about what these “pleasures” were: different readers have thus been able to find in Jekyll and Hyde allegories of alcoholism, drug abuse, homosexuality, and sexually transmitted infection.)
This is not to say that we can’t find in the novel some generalized anxiety about supposed or real scientific discoveries. Some readers have found in the descriptions of Edward Hyde echoes of Cesare Lombroso’s pseudo-scientific theory of criminal atavism:
Equating the criminal with atavism, and both with the lower classes, was a familiar gesture by the 1880s, as was the claim that deviance expressed itself most markedly through physical deformity. Stevenson’s middle-class readers would have had as little trouble deciphering the features of the “abnormal and misbegotten” Hyde, his “body an imprint of deformity and decay,” as Stevenson’s middle-class characters do. “God bless me,” exclaims Utterson, “the man seems hardly human. Something troglodytic, shall we say?”
Stephen D. Arata (1995), “The Sedulous Ape: Atavism, Professionalism, and Stevenson's Jekyll and Hyde”, Criticism 37:2, pp. 233–259.
(A ‘troglodyte’ is a cave-dweller, hence a former name for ancient humans.)
But again, even if we accept this interpretation, it doesn’t constitute an attack on science or pseudo-science: in this reading, Stevenson’s novel simply accepts as given the theory of atavism in order to exploit it as a source of horror.