I can only guess, that that has something to do with the dependency cycles.
If I render the animation and after that render a single frame, that gives a different result than when I re-open the file and then render that single frame (before ‘playing’ the animation).
(That would mean re-doing the whole rigging.)
But really, I don’t know.
It’s probably a good idea to let this rest and do some other stuff for a while.