If the content of the signs/posters includes any kind of instruction that forms part of your QMS, I would think it would be necessary to apply version control. It's also a good idea to maintain a list of locations where any signs have been put on display (with version references) so that if you update the signs in the future you can account for previous versions and replace with updated copies.
I have personally seen a food manufacturer get a non-conformity at BRCGS audit because the Food Safety and Quality Policy on display in one of the canteens was a superseded version.
I agree and would anticipate that most of OP's Posters would "by definition" be part of the FSMS although I must admit to having seen many Safety/HACCP related Posters/Banners on Production floors which were simply that, ie unversioned. And were afaik auditor uncommented.
I daresay that GFSI (rightly or wrongly) is perhaps less "stringent" on documentation as compared to, say, ISO9001 (or OSHA ?).
I guess a Policy Statement is a rather attractive/easy target.