I agree that I think they must taste bad. I have watched some wild birds eat them. My new pullets who do not have a mother hen to teach them were eating everything in sight when they were allowed to free range for the first day. I watched one bird run over to a tent caterpillar and peck at it, then it picked it up then dropped it and "washed" her beak. I think if she could spit, she would have. Another pullet saw that one, grabbed the now dropped caterpillar and did the same thing. Like most of yours, my girls are spoiled. While I do not think the tent caterpillars are poisonous, I think they are way down on the list of what tastes good and our birds will opt for many other things first. While they are always eating, they are not starving by any means. I also believe wild birds are just opportunistic feeders and therefore not as picky just to survive. They do not have the luxury of having mealworms and other goodies thrown to them regularly and and an endless supply of easily obtainable food.
At least that is my hypothesis, it is reasonable in my head so I am sticking with the plausible explanation.
And now that you have read it on the web, it is fact. Right? Ha ha...