There is only on way to get a definitive answer to Tolkien mythology questions and that is to find an answer in one of his letters. Thus this is only speculation.
- Creating new evil races is exactly what the devilish figure of Melkor did. The most offensive way to rebel against the Creator, Illúvatar.
- Men have got Fëa and hröa (approx "soul", "spirit") but Orcs do not.
- Men are not created "in the image of God" per se in Middle Earth. Their fate after death is "unknown", a mystery to all (a fact that Peter Jackson got woefully wrong).
- It is impossible to make a 1:1 mapping between Middle-earth mythology and the world view of the Bible. Shared values (mostly), but Tolkien protested vehemently when anyone tried to allegorise his writings.
In Silmarillion Eru Illúvatar (the one, the Father of all) creates god-like beings, the Ainur. They are given a beautiful song to sing, but some, led by Melkor, are rebelling and try to distort the composition. Eru, however, takes their rebellious melody and incorporates it into the final work. Then he explains that what now unfolds is the re-enactment in physical form of this.
The Ainur are very much part of the creation. One of them creates the race of the dwarves and does so too early. He is mildly chastised by Eru, that wanted the elves to come first, and the dwarves must wait a bit before their creation is complete, but Eru bestows fëa and hröa to the dwarves. (Only he can do that.)
Melkor produced creatures of his own: trolls, orcs, etc. They are totally evil, beyond any chance of redemption. They do not have an independent will (no fëa and hröa), as is evidenced by their total passivity after the destruction of the ring.
Saruman follows in the footsteps of Melkor. He produces a new, soulless and evil race. He intends to use that race to kill, plunder and scourge.
It is often made clear that in Middle-earth everything that is good and beautiful is a gift from Eru as the supreme source and the Ainur as the intermediate source. Skills and art are leaned from them, during the very first ages and from then on it is a struggle between decay and restoration.
Tolkien was in real life very much anti-modernity and it shows in the books.
Nothing Saruman did enabled the forces of decay more powerfully than creating the half-breeds. No other act of his took Middle-earth farther away from the "beautiful melody".
Even though there is no 1:1 mapping between fëa and hröa and "soul" and "spirit", no 1:1 mapping between Melkor and satan, there are similarities. There is a rebellion, a persuading others to join in that rebellion, choosing of sides between good and evil. But I can't find a distinct similarity between cross breeding orcs and humans and the Bible.