”We see here the obvious signs of internal strife, tremors and fitful convulsions, blind groping movements; unfinished sketches of failed creatures–how many terrible births and miscarriages! All these ancient animals, these antediluvian monsters: Megatheria, plesiosaurs, ichthyosaurs, pterodactyls–can they be the perfect and direct creation of God?”

Vladimir Solovyov, “Beauty in Nature”, 1889

This is a very rich question! It’s hard to generalize the reception of paleontology historically. As you surely know, there are plenty of people around today who do not believe dinosaurs ever existed, and we only have access to certain viewpoints. It’s also a little difficult to pinpoint when dinosaurs were first discovered - Greeks and Romans had seen fossils, and had some knowledge of their origins.

Richard Owen, a prolific scientist and all-around awful person, is a clear place to start, though fossils were known to the public earlier (we would then turn to Cuvier, most likely, though Paolo Rossi has an excellent book on Giambattista Vico. I’m not speaking of early modern philosophers here, but there’s plenty to say about the earliest receptions of fossils among a very small class of people). He wrote a monograph in 1841 coining the term, and for the Crystal Palace he oversaw the construction of sculptures, including those of dinosaurs, by Benjamin Waterhouse Hawkins. These sculptures were quite notable, but the handful of dinosaurs included weren’t; it was a taxonomic term without much fanfare, like Phacopida or Corynexochida are today. Nancy Marshall, a Victorian scholar, writes that

“Visually embodying the idea of the divinely ordained Great Chain of Being, the Sydenham Crystal Palace and its grounds were meant to induce reverence for the wondrous diversity of God’s universe.”

So these dinosaurs, or ‘monsters’, weren’t questioned by the Victorian public. They really had no particular reason to question them in the way you might imagine, as they still affirmed the scala naturae of Plato and Aristotle. Even Lyell uses this same language, linked quite strongly to orthogenetic evolution. Ralph O’Connor elaborates:

”The exoticism of the ancient reptiles mirrored their lowly position on the moral hierarchy, by contrast with human onlookers.”

Antediluvian is a common term you see ascribed to dinosaurs in the nineteenth century, and that may provide a way to look at how dinosaurs were received. A rich understanding of the age of the earth is a ways off, and many of the theological or spiritual problems that fossils may present aren’t present at this point, or aren’t really balanced on whether dinosaurs are a million years old or a hundred million; instead, there are evolutionary questions (which do gain purchase) about the place of humans, but dinosaurs, as ‘lesser,’ don’t raise any problems.

It wasn’t until the 1880s, with the paleontologists O.C. Marsh and Edward Cope, that dinosaurs become the cultural icons that we know. Arthur Conan Doyle’s The Lost World, for example, was written in 1912. But even as Dinosaurs begin to belong to a special category and capture public interest, there still isn’t that much objection to them never having existed. WJT Mitchell has several papers on the symbol of the dinosaur that are quite good, and Lukas Rieppel has a monograph on dinosaurs in America. The immediate reception of The Origin of Species is very complicated, and Owen himself wrote a scathing critique of it, but by the 1870s Darwinian evolution was relatively comfortably accepted by the educated Victorian public.

A rather important point that O’Connor makes is that dinosaurs weren’t simply discovered and thrust to the public for the masses to react to; rather, the public sculpts an impression of dinosaurs and a language to talk about them, as ‘monsters,’ ‘miracles,’ ‘ferocious,’ and so on. The historicity and reality of such creatures wasn’t a problem, though. The relationship between scientists and the public is similarly complicated to tease out, but it doesn’t seem at all that religious establishments were opposed to the idea of dinosaurs. After all, Darwin himself was interred at Westminster.

I'm not a religious scholar, so I can't get into why that sort of biblical fundamentalism arose, but it doesn't appear until the 1910s. Christian Fundamentalism is crystallized in the 1920s, where we get things like the Scopes Trial, well after dinosaurs were discovered and popularized.

References Marshall, Nancy Rose. "’A Dim World, Where Monsters Dwell’: The Spatial Time of the Sydenham Crystal Palace Dinosaur Park." Victorian Studies 49, no. 2 (2007): 286-301.

O'Connor, Ralph. "Victorian Saurians: The linguistic prehistory of the modern dinosaur." Journal of Victorian Culture 17, no. 4 (2012): 492-504.