The context menus are defined by the ContextMenuProvider of the xamGantt. If you want to override a context menu you would set the ContextMenuProvider to a new instance of a GanttContextMenuProvider and then set the ResourceOverrides to a ResourceDictionary that defines the xamContextMenu instance(s) for each area (defined by the items of the GanttContextMenuArea enumeration) where the x:Key is the name of the enumeration item whose area is to be overridden. If a xamContextMenu has no items then no context menu will be displayed. So if you wanted to prevent all the context menus you might do something like:

<ig:XamGantt>
    <ig:XamGantt.ContextMenuProvider>
        <ig:GanttContextMenuProvider>
            <ig:GanttContextMenuProvider.ResourceOverrides>
                <ResourceDictionary>
                    <ig:XamContextMenu x:Key="ColumnHeader" />
                    <ig:XamContextMenu x:Key="Row" />
                    <ig:XamContextMenu x:Key="RowSelectorHeader" />
                    <ig:XamContextMenu x:Key="Cell" />
                    <ig:XamContextMenu x:Key="Task" />
                    <ig:XamContextMenu x:Key="TaskDependency" />
                    <ig:XamContextMenu x:Key="Grid" />
                </ResourceDictionary>
            </ig:GanttContextMenuProvider.ResourceOverrides>
        </ig:GanttContextMenuProvider>
    </ig:XamGantt.ContextMenuProvider>
</ig:XamGantt>