When a Share is configured through the WD My Cloud Dashboard as a “Public” Share (Public Access set to On) anyone should be able to access it and create/delete folder and files on it.
When a Share is configured through the WD My Cloud Dashboard as a “Private” Share (Public Access set to Off) then each User account (in the WD My Cloud Dashboard) has to be configured for the appropriate permissions (Full Access, Read Access, No Access).
If you have not already done it is advisable to read the WD My Cloud User Manual as it explains how to configure Shares. See Chapter 8 Managing Shares for more information.
If you continue to have problems then try restarting (rebooting) both the computer’s exhibiting the problems and the WD My Cloud unit.