EditableTextBlock.cs

public class EditableTextBlock : TextBox
{
    public EditableTextBlock()
    {
        SetTextBlockStyle();
        AddHandler(PreviewMouseLeftButtonDownEvent, new MouseButtonEventHandler(ToggleTriStateFocus));
        AddHandler(LostFocusEvent, new RoutedEventHandler((sender, args) => SetTextBlockStyle()));
    }

    private void SetTextBlockStyle()
    {
        Background = null;
        BorderThickness = new Thickness(0);
        Padding = new Thickness(-2, 0, -2, 0);
        Focusable = false;
        IsReadOnly = true;
    }

    private void SetTextBoxStyle()
    {
        //Background = null;
        BorderThickness = new Thickness(1);
        Padding = new Thickness(-3, -2, -3, -2);
        IsReadOnly = false;
    }

    public static readonly DependencyProperty SelectAllTextOnFocusProperty = DependencyProperty.Register("SelectAllTextOnFocus", typeof(bool), typeof(EditableTextBlock), new PropertyMetadata(true));
    [Description("Text: string"), Category("Common Properties")]
    public bool SelectAllTextOnFocus
    {
        get { return (bool)GetValue(SelectAllTextOnFocusProperty); }
        set { SetValue(SelectAllTextOnFocusProperty, value); }
    }

    private void ToggleTriStateFocus(object sender, MouseButtonEventArgs e)
    {
        if (!SelectAllTextOnFocus)
        {
            Focusable = true;
            Focus();
            SetTextBoxStyle();
        }
        if (!Focusable)
        {
            Focusable = true;
            Focus();
            e.Handled = true;
        }
        else if (IsReadOnly)
        {
            SetTextBoxStyle();
            SelectAll();
            e.Handled = true;
        }
    }
}

Use.xaml

<StackPanel>
    <GroupBox Header="Vanilla TextBlock">
        <StackPanel Orientation="Horizontal">
            <TextBlock Text="Standard TextBlock: "/>
            <TextBlock Text="{Binding DummyText}"/>
        </StackPanel>
    </GroupBox>
    <Button>Lose focus here</Button>
    <GroupBox Header="Editable TextBlock">
        <StackPanel>
            <StackPanel Orientation="Horizontal">
                <TextBlock Text="Editable TextBlock: "/>
                <controls:EditableTextBlock x:Name="EditableTextBlock" Text="{Binding DummyText}"/>
            </StackPanel>
            <CheckBox Content="SelectAllOnFocus" 
                      IsChecked="{Binding ElementName=EditableTextBlock, Path=SelectAllTextOnFocus}"/>
            <Grid ap:Grid.Rows="Auto Auto Auto Auto" 
                  ap:Grid.Columns="auto 5 *">
                <TextBlock ap:Grid.Cell="0 0" Text="IsFocused"/>
                <TextBlock ap:Grid.Cell="0 2" Text="{Binding ElementName=EditableTextBlock,Path=IsFocused,Mode=OneWay}"/>
                <TextBlock ap:Grid.Cell="1 0" Text="Focusable"/>
                <TextBlock ap:Grid.Cell="1 2" Text="{Binding ElementName=EditableTextBlock,Path=Focusable,Mode=OneWay}"/>
                <TextBlock ap:Grid.Cell="2 0" Text="IsReadOnly"/>
                <TextBlock ap:Grid.Cell="2 2" Text="{Binding ElementName=EditableTextBlock,Path=IsReadOnly,Mode=OneWay}"/>
            </Grid>

        </StackPanel>
    </GroupBox>
</StackPanel>