Besides the Hand-Wavium of whatever the author says it is.
It is all just the power modifier you apply to the power(s) of the beast and what should affect that power modifier and their anti-thesis, and/or it has been shaped by said powers.
Demonic Beasts are affected by holy power and produce effects that are demonic based. A techno beast should be affected by anti-technology devices/powers and produce technological effects. A Soul beast has soul powers and should be affected by Soul affecting powers. A Holy Beasts Anti is Demonic powers and they use Holy abilities. A Magic Beast has or is affected by "Magic".
Now "Spirit Beast" is a really broad term that can cover a lot of the above beasts and other things, even in the same novel. Spirit beasts tend to be affected by or effect things depending on what the author decided their type of spirit category it is: Usually if further defined, it could be Magic, Chi, Undead (Ghost type), or Soul effects. Or any combination thereof, and a few things I have not mentioned.
The type of Beast could be cultural and have no real affect on anything.
Your intrepid hero, while staying at her latest harem acquisitions house. Hears of a Tiger that has been eating villagers. It is of course a Demonic Tiger that eats humans for its powers when it is talked about; but in reality it is just a Tiger that finds humans easy prey. It all depends on the narration of the story.
Wherever humans and large predators come together there are often bound to be what are called man-eaters, those individuals
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