How to avoid Converters clashing with multibinding in WPF code behind

It's relatively easy. Everything should resolve around CheckBox IsChecked property. For a simple reason, it's a two-way property. So either you can modify it, or CheckBox can modify it.

So what you do, you use MultiBinding, as such:

    MultiBinding multiBinding = new MultiBinding();
    multiBinding.Converter = multiBindingConverter;

    multiBinding.Bindings.Add(new Binding("Text") { Source = txtbox1});
    multiBinding.Bindings.Add(new Binding("Text") { Source = txtbox2});

    multiBinding.NotifyOnSourceUpdated = true;//this is important. 
    checkBox.SetBinding(CheckBox.IsCheckedProperty, multiBinding);

And in your multiBindingConverter, you will have object[] value as first parameter, which you need to convert into IList and iterate over it && do your calculations, if you should either return true/false.(IsChecked=true or false)

Now bind CheckBox IsEnabled to CheckBox IsChecked property, and use BooleanInverterConverter. (If CheckBox is checked, it should be disabled, and vice versa)

The last step is to make TextBoxes listen to actual IsChecked property of CheckBox. If it is TRUE, they all should show value of 0, otherwise they can show what they want.

So, make a new MultiBinding.

    MultiBinding multiBinding = new MultiBinding();
    multiBinding.Converter = textboxMultiBindingConverter;

    multiBinding.Bindings.Add(new Binding("IsChecked") { Source = checkbox1});
    multiBinding.Bindings.Add(new Binding("Text") { Source = textbox1});

    multiBinding.NotifyOnSourceUpdated = true;//this is important. 
    textbox1.SetBinding(TextBox.Text, multiBinding);

the idea in textboxMultiBindingConverter is to either return Text(value[1]) if value[0]==FALSE or "0" if value[0]==TRUE.