Opinions (and Houserules) differ widely - and I can say with some confidence that bc this was kicked around not long ago: https://forum.atlas-games.com/t/a-staff-in-any-other-shape/6162/1
(The OP in that thread addresses only Talismans, but the thread expands to consider the broader question that you are asking)
In short, for many posters, it seems to come down to "True Nature" - what the thing is, before (Muto) magic changes it. So, by this view, a ring changed to a bow is still a ring for most all magical purposes, and similarly a bow changed to a ring is always a bow. (Sim for material.)
From a purely game-balance perspective, while a 2-shape item is not a headache, a stronger Muto effect could allow any number of shapes and/or materials, and that opens the door to a lot of abuse - for some SG's. Others welcome such "creativity" - ysmv.