Disable selecting in WPF DataGrid

The clean way would be, to just override the styles of the row and the cell

<DataGrid.Resources>
    <ResourceDictionary>
        <Style x:Key="{x:Type DataGridCell}" TargetType="{x:Type DataGridCell}">
            <Setter Property="Background" Value="{x:Null}" />
            <Setter Property="BorderBrush" Value="{x:Null}" />
            <Style.Triggers>
                <Trigger Property="IsSelected" Value="True">
                    <Setter Property="Background" Value="{x:Null}" />
                    <Setter Property="BorderBrush" Value="{x:Null}" />
                </Trigger>
            </Style.Triggers>
        </Style>
        <Style TargetType="{x:Type DataGridRow}">
            <Setter Property="Background" Value="{x:Null}" />
            <Setter Property="BorderBrush" Value="{x:Null}" />
            <Style.Triggers>
                <Trigger Property="IsSelected" Value="True">
                    <Setter Property="Background" Value="{x:Null}" />
                    <Setter Property="BorderBrush" Value="{x:Null}" />
                </Trigger>
            </Style.Triggers>
        </Style>
    </ResourceDictionary>
</DataGrid.Resources>