There are many ways to do this, but the easier way is to refer with DynamicResource.
<DataGrid x:Name="dataGrid1" >
<DataGrid.Resources>
<SolidColorBrush Color="Black" x:Key="columnForeground"/>
</DataGrid.Resources>
<DataGrid.Columns>
<DataGridTemplateColumn Header="Nr " Width="38" CanUserSort="True" x:Name="SP001" >
<DataGridTemplateColumn.CellTemplate>
<DataTemplate >
<Label x:Name="SP001F"
Height="50"
Content="{Binding GrLaufendePosition}"
Foreground="{DynamicResource columnForeground}"
Background="White"
HorizontalAlignment="Center"
HorizontalContentAlignment="Center"
VerticalContentAlignment="Center"
BorderThickness="0"
VerticalAlignment="Center"/>
</DataTemplate>
</DataGridTemplateColumn.CellTemplate>
</DataGridTemplateColumn>
</DataGrid.Columns>
</DataGrid>
this.dataGrid1.Resources["columnForeground"] = Brushes.Red;