I failed with the control TextBlock, so I used the disabled. TextBox
You can change the template TextBox, I want to remove the border and set its background to be really transparent.

<sdk:DataGrid AutoGenerateColumns="False" ItemsSource="{Binding Items}" IsReadOnly="False" SelectionMode="Single">
<sdk:DataGrid.Columns>
<sdk:DataGridTextColumn Header="Title" Binding="{Binding Title}"/>
<sdk:DataGridTemplateColumn Header="Link" Width="100">
<sdk:DataGridTemplateColumn.CellTemplate>
<DataTemplate>
<TextBox Text="{Binding Link, Mode=TwoWay}" Margin="2"
IsEnabled="False" BorderThickness="0" Background="Transparent"/>
</DataTemplate>
</sdk:DataGridTemplateColumn.CellTemplate>
<sdk:DataGridTemplateColumn.CellEditingTemplate>
<DataTemplate>
<TextBox Text="{Binding Link, Mode=TwoWay}" Margin="2"/>
</DataTemplate>
</sdk:DataGridTemplateColumn.CellEditingTemplate>
</sdk:DataGridTemplateColumn>
</sdk:DataGrid.Columns>
</sdk:DataGrid>
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