When logged in as operator and using find tool to search for an object, we can right click on the found object
What permissions have you given the operator user (in context menu of found object, select Details..., then click the Permissions tab)?
Drag & drop (e.g. needed to export) can be blocked by declining "Modify" permission on the structure where the object is located. Structure permissions are set in the Aspect System Structure -> ... -> xxx Structure -> Aspect Category -> Role Bindings
It sounds like the user have too high roles and permissions...
You are correct, The context menu for the results in Find tool do not care about the user security. It means that, no matter which user you log in as, you will still get the same options.
But 800xA system security will take care if the user triggers any action from this menu. So even if you get the options to delete/release/export, as an operator ( who is haveing only operator role), you can not "release" or "delete" something.
So no harm...