1. Herons are predators, not vegetarians.
An egret's diet consists of fish, frogs, and bugs. I see pairs of them hunting in the water near our bus stop, and they're definitely trying to grab something with their sharp beaks. Those things aren't for show. (Proof!) I've never seen one scavenge for berries-- just saying. Their calls, while not actually ugly or abrasive, aren't any more sing-songy than the ones my cat used to make when she got all excited over the birds outside the window.
To be honest, when this conversation happens in PoR--
Ike: As long as you take care of yourself, I have no complaints. But isn't there anything I can do to help? Maybe we could have a special supper. Certain foods tend to restore energy.
Reyson: That's very kind, but my diet... Heh. It's fairly limited. You know, I used to be disgusted by my thin, frail body. So one time I performed a little experiment. I got all the foods that Tibarn likes-- raw meat, cold fish, insects--and ate them. I ate them all.
Ike: That doesn't sound good. What happened?
Reyson: I stared death in the face for ten days. You've never seen a laguz so green! I guess we herons are just meant to eat fruits and nuts for our entire lives.
--my first thought is, "Well yeah, if you eat RAW MEAT when you usually don't consume any kind of meat at all, of course it's going to make you sick." Besides that, all sorts of bacteria come with raw meat-- come on. What would've happened if Reyson ate cooked meat, or cooked fish, or specially prepared raw fish? Some fish and meats are more easily digested than others. For that matter, some vegetables and plant matter are ridiculously hard on one's system.
I figure we all already know this. The question is, why?
Which brings me to point two, which I've mentioned before, but which has special bearing on this topic:
2. The herons are clearly "inspired" by Tolkien's elves.
Visually, that is. You might say this explains why FE's herons can't eat meat - on the surface the elves look pretty vegetarian. When I was looking up notes on elven eating habits - and you bet information like that exists! Ah, Tolkien - quite a few people had the same idea, because they're so attuned to nature. Supposedly. But when the question gets asked on forums, the conclusion is usually that yes, even Tolkien's elves eat meat. They enjoy hunting. Killing animals for sport and not using the meat or the rest of the carcass (say, deerskin), is even less in line with their apparent nature than chowing down on venison. Also, this quote came up:
From the Hobbit - Flies and Spiders
There was a fire in their midst and there were torches fastened to some of the trees round about; but the most splendid sight of all: they were eating and drinking and laughing merrily. The smell of the roast meats was so enchanting that, without waiting to consult one another, every one of them got up and scrambled forwards into the ring with the one idea of begging some food.
While I came across other quotes, this one was the most direct. Another good one is from the Lay of the Children of Hurin:
On a time was Turin at the table of Thingol
there was laughter long and the loud clamour
of a countless company that quaffed the mead,
amid the wine of Dor-Winion that went ungrudged
in their golden goblets; and goodly meats
there burdened the boards, neath the blazing torches
Hunting game was a respectable pastime back in the day, so speculation says the elves probably ate venison, rabbit, boar, wild birds, etc. I could swear I saw a mention of elves serving excellent salt pork, but I can't find it now. So in any case, some of Tolkien's elves eat meat. Really good meat. Enchanting meat. It could be that he changed his mind about that later, but I can't recall anything that would make me think so. More informed readers might have a better idea of what the author wanted. I think it's arguable, though.
And let's not forget that elves are stronger and hardier than men, which FE's herons are most definitely not.
So: if it's not Tolkien's influence that inspired the designers to make herons vegetarian, what did? I have an idea, inspired by a base conversation before/during 4-F-4 in Radiant Dawn:
Lehran ... attempted suicide several times, which is an unthinkable taboo for anyone who has sworn to serve the goddess.
If taking one's own life is unthinkable, it isn't much of a stretch to speculate that those dedicated to Ashera's service simply don't take any lives at all if they can help it. I've had this in my headcanon for a while: characters like Sanaki almost never eat meat in my stories because they're dedicated to the goddess and her tenets, and one of those is the sanctity of all life-- maybe. We don't really know, but that's how I read it.
Nasir has already commented on the piety of the Serenes herons. My theory is that they abstain from meat voluntarily, but that they are not physically incapable of eating it. Now, if you just don't eat meat, ever, then trying to have a steak for dinner will probably wreak havoc on your digestive system-- but that doesn't mean you're incapable of consuming it by nature.
Let's also keep in mind that hawks generally don't eat pastries, and yet Phoenicis apparently makes some awesome desserts. Just throwing that out there.