Gantt tasks which are representing Jira versions or components have an icon of crossed circle which doesn't allow to drag and drop it on the gantt or to the change of task mode.
The user viewing the Gantt has no permission to administer the Jira project in which the issue is registered.
Full description about Jira Project permissions and their effects can be found here. This page includes the information about "Administer project" permission influencing the version and components management.
Ask your Jira admin to grant the Administer projects permission to project in which you would like to manage versions and/or components via Gantt.