Users with "Edit [Main Entity Type]" permissions can modify any field shown on the Checklist, except the Response Time. This allows the users to re-asign tasks to other users and modify the due dates, without Full Admin permissions.
If user's mishandling the Due Dates is a concern for your Organization, then you can setup a special Modification History report thats filtered on the "Due Date" field and where the Old Value is not empty, which will allow you to track users editing the Due Dates.
Editing Individual Due Dates for Manually Entered Items
Users can enter tasks with due dates for themselves to create reminders for a record. Administrators can add tasks to any checklist at any time for any user. Non-admin users can enter the Response Date and can change checklist item names and Due Date for items that they entered themselves. These users cannot modify the Due Date or Responsible Worker for Checklist Items that are auto-entered. The only way to circumvent this Due Date restriction is by linking up Due Date and Completed Date Fields.
Editing Automatic Due Dates
Only Full Admins can enter or edit the Due Date and the responsible user for checklist items that are auto-entered from the Checklist Configuration.