@lindsayt A quick guess is that the references from the bundled skeletons to the shader (or Material) are referencing a new asset reference, while the target of the reference are in an asset bundle which is either not loaded when loading the skeletons, or perhaps has not been re-generated with the new shaders and materials. So in other words, it sounds as if the packages containing the references don't match the available packages containing the referenced asset, either of the two seem to have been missing an update. You could have a quick try whether putting the shader into the same bundle as the problematic skeleton resolves the issue for this skeleton. Or you could also add the used shaders to the Always Included Shaders in the Project Settings.
Or there is a race condition that the skeletons are loaded before the shaders and materials, and the dependency order is not maintained (for whatever reason).
You could also check in your used version control system whether the .meta files (and therefore the GUIDs) of the used shader or materials have been modified.