well then - help me out :)
I've re-read your post several times.
"Religious prescription makes it possible for otherwise not cruel people to make animals suffer. Blurring the distinction is not helpful or smart in any way."
I think there exist valid distinctions; e.g. a vet who needs to make an animal suffer temporary pain while providing long term relief is an important distinction.
However, what I've put forward is that currently, we are giving TOO much credit and distinction for people who desire cruelty upon animals (and many other things) due to religion alone; vs other arbitrary personal desires and preferences. I think we need to blur that distinction, or support it with something else than "because religion".
In other words, to me:
Group A: Inflicts temporary pain to animals for purpose of long term relief or some other quantifiable objective benefit to something or somebody somewhere
Group B: Inflicts pain to animals for no good reason / for enjoyment of cruelty / for fun / for religion. I deny your claim that people who desire harm upon animals for religious reasons alone, are "otherwise not cruel people". I think "Cruel" is precisely what they are, and I deny them using religion as valid ethical excuse that means anything else than "because I wanted to", because religion is freely chosen and freely obeyed and we remain agents of free will. Or to put it another way - what about humans? If people want to harm other humans for only religious reasons, are we still treating them as "otherwise not cruel"?
I'm willing to listen what your alternative hypothesis/point/statement is - why are people who desire cruelty upon animals for religious reasons alone "not otherwise cruel", or how DO you narrowly define cruelty then?
(and again, it took me personally 30 years to stop giving religion a culturally-conditioned, social-norms free pass on these things; and I still have to fight this ingrained reflex to not instinctively believe that "because religion" is a superior reason to "because I want to". I don't expect anybody else to make that journey in 15 minutes debating internet strangers even if they want to).
[Final note: IF your point is more along the lines of "we should understand the details of reasoning and motivations", absolutely; but I did not see that line of reasoning in your original post. My point is I see no moral distinction or superiority between "because religion" and "because I want to", and one should not be given more credence than the other -- which is not to deny that understanding the motivations in detail is a useful and positive effort]