Not sure exactly what particular FabTab functionality you are looking for in your app, but if you set ShowContentsTab="False" on the FabTabControl you declare in your ShellView.xaml then it all works beautifully.
Of course you won't have the ContentTabView then. The problem I am seeing makes perfect sense--you're correctly trying to bind the ItemsSource of FabTab to a BindableCollection<IScreen> off of the Conductor, but then when I try to "trick"
FabTab into adding the ContentTabView in behind the scenes we get that Exception because ContentTabView doesn't implement IScreen and can't be added to the Collection.
There's a number of ways to solve this. One would be for me to somehow allow the FabTabConsumer to create their own sort of ContentTabView which could then be made to implement whatever interfaces are necessary. I suspect that would be fairly
involved. You'll notice that anywhere in the FabTab Sample project where I use the ItemsSource to populate the control I bind to ObservableCollection<object>; That allows me to add in ContentTabView behind the scenes and have it work. But that's
not a great solution is it? let me think about that
Another would be for you to modify the FabTab source to make ContentTabView implement IScreen...that's the beauty of open source, you have the ability to create your own version of FabTab which references Caliburn Micro and does what you need.
I'll keep you posted on my thoughts about this as I poke around. Let me know if you have any ideas or whether you even care about the ContentTab functionality.