The only way I got it to work is by setting the columns by myself, (by not using AutoGenerate). So first thing to do is define the columns:
<DataGrid x:Name="Frid" ItemsSource="{Binding Path=.}">
<DataGrid.Columns>
<DataGridTextColumn Header="First Name"
Binding="{Binding Path=FirstName}">
</DataGridTextColumn>
<DataGridTextColumn Header="Last Name"
Binding="{Binding Path=LastName}">
</DataGridTextColumn>
</DataGrid.Columns>
</DataGrid>
Then you need to set each column CellStyle and bind the Background to a static resource that you can declare at Window.Resources:
<Window x:Class="WpfApplication1.MainWindow" ...>
<Window.Resources>
<SolidColorBrush x:Key="clBr" Color="White" />
</Window.Resources>
...
Columns:
<DataGridTextColumn Header="First Name"
Binding="{Binding Path=FirstName}">
<DataGridTextColumn.CellStyle>
<Style TargetType="DataGridCell">
<Setter Property="Background"
Value="{StaticResource clBr}" />
</Style>
</DataGridTextColumn.CellStyle>
</DataGridTextColumn>
then you can just manipulate the static resource by either code or xaml manipulation.
Hope it helps.