That's almost certainly correct. Another way to view it is as a matter of community: "We are the people who don't eat X (or wear X, or do X)". Much as Americans view people who eat dogs as repulsive, having a set of proscribed behaviors defines who you're not and thus who you are.

When it comes to eating dog, the prohibition feels nearly as strong as if it came from God. It would take only a little nudge for somebody's existing dietary preferences to become scripture.

That preference might have had some other kind of more immediate necessity as well, but a lot of such cultural dictates are either arbitrary or become arbitrary as circumstances change. That just makes the cultural marker even more imperative. It would be easy to avoid pigs, say, if they were actually bad for you. Avoiding them even when everybody else is consuming them successfully shows a real determination.

The cultural angle is covered near the end of the video (around 11 minutes). Apparently there is some evidence northern Israelites were still eating pork and the rules became a way to bind everyone together culturally, though like all other reasons there's no hard evidence.

"Protein poisoning (also referred to colloquially as rabbit starvation, mal de caribou, or fat starvation) refers to an unverified acute form of malnutrition that some have speculated may be caused by a diet deficient in fat, where excessive lean meat is consumed", from https://en.wikipedia.org/wiki/Rabbit_starvation

This sounds like confirmation bias, though (you can find a reason not to eat anything if you look closely enough). It is also highly speculative.

I think from an ethnographic point of view, cultural reasons are perfectly plausible, in the same way some people now refuse to eat horse, veal, or indeed rabbit.

Perhaps God's prophet was a chicken farmer.