If archival and acid free hinges are used to attach the poster to the acid free backing board with an archival adhesive, (like those used on expensive etchings, for example, when framed), these should pose no problem or cause damage or staining to any kind of poster.
But like anything, it all depends on making sure that the proper materials are used by a framer. And if one thinks that they may swap out posters in that frame, then this may not be the best method.
But if in a permanent frame, i would think it would be fine.