It’s wrong after it’s dead because it’s disrespectful to the deer, which was once a living being.

But people eat the deer with zero moral qualms. Are you really going to tell me that yanking something's skin off, cracking its bones, gouging out its internal organs, and processing its meat into sausages for roasting is a sign of respect?

I don't think you'll get consensus on the "it's disrespectful" reasoning. It might not be inherently religious (although most religions I'm aware of expand upon it to specific procedures or prohibitions) but "respecting" the vessel which once contained a life seems very much tied up in sentimentality and woowoo more than sound reasoning or pragmatism. It's just engrained into social norms at this point but, purely speculation, burial and burning were probably done for the same reasons other animals do it - you don't attract other predators or suffer the scent of death inviting maggots, flies and other vectors for disease. It probably became more ritualistic and religious over time. If I'm dead someone can dangle my lads from their rearview like a pair of fuzzy dice for all I care - which will be not at all because I'm dead.

well, why is it we shouldn't disrespect? don’t get me wrong, i agree that we should respect, but many customs of respect like this one seem to have origins nearly as arbitrary as faith

I mean there are evolutionary reasons most humans feel disgust towards things, in this case mainly the spread of disease. If none of these were problems, there isn't really a good moral case to be made against it unless you believe in some sort of afterlife.