I don't think so. I've used rust converter and it doesn't affect paint at all. Naval jelly is strong, so it might. I'd search for phosphoric acid on BF to make sure.

Vinegar and old rags shouldn't hurt the paint. Dilute a bit if necessary, but I find most vinegar is dilute enough. Aluminum foil I just tend to concentrate around rusted bare steel - twist it into a point and rub. It will take off the paint if you rub it at a painted spot.