In short, it's not that we were 'designed' for anything. There have been times where humans have been 'selected' for some characteristic, but that doesn't mean that being an omnivore (or storing fat) is prosurvival now, much less that it is in any manner imperative.
From wikipedia: On the average, 1 person dies every second as a result, either directly or indirectly, of hunger - 4000 every hour - 100 000 each day - 36 million each year - 58 % of all deaths (2001-2004 estimates)
I'm pretty sure if we are only carnivore or herbivore this number would have risen because that simply mean we have less access to food. YOU who can afford an internet connection may not feel the need for it, but many does.
I'd make a less extreme example: outdoor survival. Many have had to endure days or months in the wild and had to secure food for themselves. And according to military procedures, it's takes less time to procure surely non-poisonous animal-derived food while plant-derived chows are more abundant. Each has its own strength and having 1 more option is always better.
Aside from intolerance, are there any reasons you listed cannot be considered as groundless belief?
EVERYTHING can be properly considered a "groundless belief". "God told me not to eat of animals unless they had cloven hooves and chew their cud." is just as valid as "Animals have a right to not be killed on my behalf." or "It is important that I procreate efficiently." or even "All people are equal in rights."
As I have mentioned above, if anything can be why-traced back to proven factual science then it's not groundless. Many are not easy to boil down that way of course, that's why we have debates. It's also depending on the scope of the conversation. In example, "all people are equal in rights"is debatable. It is a good thing in small communities where it's possible to assume everyone are more or less equal in knowledge. When you have things like idiots voting one big idiot to be their president then it's probably not a good thing for the community to survive. However things such as "It is important that I procreate efficiently" is not groundless. Without efficient procreation, human race will have no future.
EDIT: I need sleep. Basic need > self-actualization.