How can I prevent a ToggleButton from being Toggled without setting IsEnabled

You can override the OnToggle method to prevent toggling the state, by not calling the base implementation :

public class LockableToggleButton : ToggleButton
{
    protected override void OnToggle()
    {
        if (!LockToggle)
        {
            base.OnToggle();
        }
    }

    public bool LockToggle
    {
        get { return (bool)GetValue(LockToggleProperty); }
        set { SetValue(LockToggleProperty, value); }
    }

    // Using a DependencyProperty as the backing store for LockToggle.  This enables animation, styling, binding, etc...
    public static readonly DependencyProperty LockToggleProperty =
        DependencyProperty.Register("LockToggle", typeof(bool), typeof(LockableToggleButton), new UIPropertyMetadata(false));
}

Have you tried using RadioButtons instead? It normally can't be deselected without selecting another one. It can also be styled to look like a ToggleButton:

<RadioButton Style="{StaticResource {x:Type ToggleButton}}"/>

Or, if you already have a Style for it, just make it BasedOn="{x:Type ToggleButton}". Note that the Visual Studio Editor shows an error in the first case, but it compiles and works fine.

This is hackey, but if you don't want custom code you could always use the property "IsHitTestVisible", when you don't want them to uncheck it, simply set IsHitTestVisible equal to false. However, they may be able to tab to the control and toggle it using the space bar.