Non administrators (with reviewer, contributor and editor role) unable rearrange order of items in folders

I keep getting "error: item not moved". I thought they would have had enough permission to do this.
What permission am I missing?

any luck on this? I'm seeing you didn't get any help and willing to dig in if you need.

There's not much information to work with but if you installed any Plone add-ons which register subscribers on one of the object events, those may raise an error for the user in question.

As a manager, you can access the ZMI error log at https://yoursite.tld/error_log/manage_main, in the "Ignored exception types" field, add a # before Unauthorized and "Save changes", reproduce the "error: item not moved" error and return to the ZMI error log (or use the one in the Plone control panel), a more verbose error should show up that can help in identifying the issue.