Kane generally referred to most of the supernatural things he was up against as being hellish and Satan-spawned, just like real-world Puritans conflated any form of paganism with devil worship. Puritanism made it simple: if it's not of God, then it's witchcraft.
And yet, in "The Footfalls Within", he realises that there exist creatures and things outside this frame of reference, such as the Horror, or, I think, the Staff of Solomon.
There's also the fact that Howard (an agnostic, as I recall) chose not to include explicitly Christian supernatural elements in the stories, opting for black magic and hints of something vaguely Lovecraftian, despite his main character being a Puritan and repeatedly mentioned to be such. To the reader, an outside observer, there is no proof that what he believes is in any way real, and there are in fact hints to the contrary (For one thing, I'd consider the monotheistic Christian view and Cthulhu Mythos mutually exclusive as true in the same diegetic frame - the first one kinda defines its god as the only god and the second one hinges on the assumption that there are many gods and none of them are what you'd call nice - of course, this is all in how great conclusions one is willing to draw from "The Footfalls Within", Howard's agnosticism and ties to the greater body of his work. I think much could be written about this.).
Our recollections of Howard's depiction differ somewhat, as the most striking detail of Kane was that at his core, he was no true Christian. He was born out of his proper time, a larger-than-life hero in a world where such men had become all but extinct, and Christianity was just an engrained affectation that allowed Kane to come to terms with his nature.
I'd rather not enter a debate as to what constitutes a true Christian, especially on these forums. The history of Europe runs red with such debates. Yes, Solomon Kane was a bit of a throwback to the age of Conan, but he had faith and he kept it, even if what actually kept him going was a superhuman willpower and physique and an atavistic urge to stuff someone's own kidneys down their throat.
You seem flatly unappeasable, having reduced this whole thing to a binary equation. Taken to its logical extent, this suggests there's no way to build on Kane's canon--the only option is to simply regurgitate a Howard story word-for-word, detail-for-detail, buckle-for-buckle.
Well, that is, in a way, true. The core of the Solomon Kane canon has been written and cannot be added to, seeing as Robert E. Howard has lain in his grave these past 70 years or so. Whatever anyone else does with his characters will be by definition a derivative, lesser work (a great deal lesser, in many cases).
However, there are still derivative works that I can approve of, and I tend to rate these in terms of faithfulness to the source material and quality. Arnie's first Conan film qualifies despite diverging occasionally from the stories and yoinking a villain from a Kull story because it is a very good film. The second one doesn't, because it sucks. Red Sonja can burn, though the character is so very far removed from Howard's work that no meaningful comparisons can any longer be drawn and she fails entirely on her own lack of merit.
I have, for the most part, refrained from commenting on the story itself, not only because it's still for the most part unknown but also because the episodic nature of the pulp heroes lends itself well to the adding of new tales, and there is nothing wrong with it - as long as it is done well. What we know of the character, though, leads me to believe that Bassett's
Solomon Kane has no more to do with Howard's Puritan swordsman than Sommers'
Van Helsing had. There's more to Howard's character than the hat, and especially the AICN review contains details that run directly contrary to the character. So, it can still be a good fantasy action movie, but it doesn't look like much of a Solomon Kane film.
It all just leads me to wonder why take the name if you won't use the character, especially when the character is so little known that you can't really sell the movie with it, or even the author's name, and will only end up pissing off the hardcore fans.