I'm not certain why this is happening. My simple bat animation looks correct when I do the viewport render or scan through my timeline. As soon as I tell Blender to render it, the bones and skin of the wings are out of sync.
Renders below.
Looks right in the viewport render: https://youtu.be/vCcE-vW6uAE
Bones and skin out of sync when doing the render: https://youtu.be/2WSX5UOYD_I
I'll look for possible answers as well, and if I find them I'll post here, but if somebody already knows how to resolve this I'm all ears.
Nevermind, I found it. I had a shrink-wrap modifier I was trying to use to stick the wings to the bones, but it worked better without it.
I had turned the shrink-wrap off everywhere except the final render. Just deleting the modifier resolved the issue.