In general, raw green beans are always nutritious, though some other kinds of raw beans have a lot more hemagglutinin, which is a mild poison. I haven't grown green beans in a while, but I remember that birds stealing them was an issue. Clearly, they will snap up bean seeds. To some extent, they'll even eat the leaves.

Are the tiny immature beans showing signs they were picked or chewed off? Anything on the ground under the vines to indicate they're dropping by themselves?

Nope, nothing on the ground. The immature beans aren't half-chewed or anything, the ones I've seen are intact.

I've had birds go after baby pea pods.... so why not baby beans.

Maybe some row covers are in order?

FWIW, I had a problem with my blackberries earlier this year and used a bolt of sheer nylon/polyester drapery fabric to basically wrap the patch to keep the birds off. The fabric is sheer enough to let in sunlight. Since beans don't need pollinators, covering may solve the issue.

The trellises (cattle panels, actually), are over 6' tall -- covering wouldn't be an easy task, nor would uncovering to harvest every few days.

IMO birds are unlikely to be the problem. I would first suspect that heat stress and/or water stress is causing the flowers & young pods to abort. That is a fairly common issue with beans, especially in the dog days of summer. It may help to spray the vines down briefly in the afternoon on sunny days, when the plants are under the most stress. If the plants are not mulched around the base to retain moisture & cool the soil, doing so may also be helpful.

I have seen rodents climbing a trellis and eating beans. Do you have chipmunks or mice?

I think this site might refer to feeding pet birds, but ...

https://crittercleanout.com/can-birds-eat-green-beans/

As I said, I have seen them raid my plants.

Yes, aborting is a possibility, but then you're going to see remnants of those aborted beans on the soil.

Another possibility is too much nitrogen. I did this unintentionally, but should have known better. I planted bush green beans in between mounds of watermelons and the high fertilizer initially caused mega-growth of leaves and tall gangster growth of the plants. They are finally putting on a lot of blooms, but it took awhile!

That's true, mxk3. I just checked and I do have some beans coming on. Maybe they are just slow.

Okay......looking in a different direction. When I grew pole beans several years ago, and it was consistently VERY hot out, they never made beans. Has your weather been really hot? I couldn't believe how nice my pole bean leaves were.........just no beans. And if you had animals/birds eating them, they would leave half-eaten beans. I've just never seen that happen in my rural garden.

The temps have been up and down, many days in the high 80s/low 90s and h-u-m-i-d. So maybe that's it...

I have beans! I have beans! WooHoo finally! Maybe it was just the weather, don't know {shrug}.

We picked some too! Finally, huh?! What kind are you growing? Mine are Blue Lake Bush, but look more like climbers after all the nutrients from the watermelon. They do look really lush and healthy though!