This suggestion does not work.

You don't need all the code behind at all.

Just do

<igRibbon:XamRibbon.Resources>

<Style TargetType="{x:Type ribbon:RibbonContextMenu}">
            <Setter Property="Visibility" Value="Collapsed" />
        </Style>

</igRibbon:XamRibbon.Resources>

Thanks for the solution.  In my case, I have disabled the QAT and collapsed it as well.  In short, I don't the users to be able to interact with it at all.  As a result, I have extended the solution to remove all references to the Quick Access Toolbar in the XamRibbon content menu.  Now, the only menu item that shows is the Minimize Ribbon menu item.

public void RibbonContextMenuOpened(object sender, RoutedEventArgs e)
{
    var menu = item as RibbonContextMenu;
    if (menu == null) return;
    // Loop to remove all menu items that reference the QAT
    while (true)
    {
        var removeIndex = -1;
        foreach (var item in menu.Items)
        {
            var menuItem = item as ToolMenuItem;
            if (menuItem == null) { continue; }
            if (menuItem.Header.ToString().Contains("Quick Access Toolbar"))
            {
                removeIndex = menu.Items.IndexOf(item);
                break;
            }
        }
        if (removeIndex == -1) { break; }
        menu.Items.RemoveAt(removeIndex);
        menu.Items.RemoveAt(removeIndex);  // removes trailing separator
    }
}

Thanks for your assistance!  That resolved the issue.