On a multi-user system, the ID which created a template was able to import the template under manage templates however, a different ID was not able to import the template even though all IDs have permission to update the template (mode is rw-rw-rw or 666).
Read-permission is one thing - but doesn’t import mean that the template is to be stored into the path given in Tools -> Options -> LibreOffice -> Paths -> Type: Templates and did you check also write permission of “different ID” into the given template directory?