I needed a selectable TextBlock to show some id. However a TextBlock is not selectable so I made a TextBox look like a TextBlock. A TextBlock is selectable..
You only need the properties 'Background' and 'Border':
<TextBox x:Name="textBlockProductId"
Background="Transparent"
BorderThickness="0"
Text="{Binding SelectedProductId, Mode=TwoWay, UpdateSourceTrigger=PropertyChanged}" />
That's it, your TextBox will look like a TextBlock!