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If you want to change the Background of DataGridColumn.Header, you need to change its default Style. From the default Style, there is a line which define the background of the Header:
<Rectangle x:Name="BackgroundRectangle" Stretch="Fill" Fill="{ThemeResource DataGridColumnHeaderBackgroundBrush}" Grid.ColumnSpan="2"/>
So if you want to change the background, you can change the value of DataGridColumnHeaderBackgroundBrush or define a Background property and bind the property with this Fill property. For example, I define a Background property in Style of DataGridColumnHeader.
.xaml:
<Page.Resources>
<ResourceDictionary>
<ResourceDictionary.ThemeDictionaries>
<ResourceDictionary x:Key="Default">
<SolidColorBrush x:Key="InvalidBrush" Color="#FFFF00"/>
<SolidColorBrush x:Key="FillerGridLinesBrush" Color="Transparent"/>
<StaticResource x:Key="ScrollBarsSeparatorBackground" ResourceKey="SystemControlPageBackgroundChromeLowBrush"/>
<StaticResource x:Key="DataGridColumnHeaderForegroundBrush" ResourceKey="SystemControlForegroundBaseMediumBrush"/>
<StaticResource x:Key="DataGridColumnHeaderBackgroundColor" ResourceKey="SystemAltHighColor"/>
<SolidColorBrush x:Key="DataGridColumnHeaderBackgroundBrush" Color="Red"/>
<StaticResource x:Key="DataGridColumnHeaderHoveredBackgroundColor" ResourceKey="SystemListLowColor"/>
<StaticResource x:Key="DataGridColumnHeaderPressedBackgroundColor" ResourceKey="SystemListMediumColor"/>
<StaticResource x:Key="DataGridColumnHeaderDraggedBackgroundBrush" ResourceKey="SystemControlBackgroundChromeMediumLowBrush"/>
<StaticResource x:Key="DataGridColumnHeaderPointerOverBrush" ResourceKey="SystemControlHighlightListLowBrush"/>
<StaticResource x:Key="DataGridColumnHeaderPressedBrush" ResourceKey="SystemControlHighlightListMediumBrush"/>
</ResourceDictionary>
<ResourceDictionary x:Key="HighContrast">
<SolidColorBrush x:Key="InvalidBrush" Color="#FFFF00"/>
<SolidColorBrush x:Key="FillerGridLinesBrush" Color="Transparent"/>
<StaticResource x:Key="ScrollBarsSeparatorBackground" ResourceKey="SystemControlPageBackgroundChromeLowBrush"/>
<StaticResource x:Key="DataGridColumnHeaderForegroundBrush" ResourceKey="SystemControlForegroundBaseMediumBrush"/>
<StaticResource x:Key="DataGridColumnHeaderBackgroundColor" ResourceKey="SystemAltHighColor"/>
<SolidColorBrush x:Key="DataGridColumnHeaderBackgroundBrush" Color="Red"/>
<StaticResource x:Key="DataGridColumnHeaderHoveredBackgroundColor" ResourceKey="SystemListLowColor"/>
<StaticResource x:Key="DataGridColumnHeaderPressedBackgroundColor" ResourceKey="SystemListMediumColor"/>
<StaticResource x:Key="DataGridColumnHeaderDraggedBackgroundBrush" ResourceKey="SystemControlBackgroundChromeMediumLowBrush"/>
<StaticResource x:Key="DataGridColumnHeaderPointerOverBrush" ResourceKey="SystemControlHighlightListLowBrush"/>
<StaticResource x:Key="DataGridColumnHeaderPressedBrush" ResourceKey="SystemControlHighlightListMediumBrush"/>
</ResourceDictionary>
<ResourceDictionary x:Key="Light">
<SolidColorBrush x:Key="InvalidBrush" Color="#C50500"/>
<SolidColorBrush x:Key="FillerGridLinesBrush" Color="Transparent"/>
<SolidColorBrush x:Key="ScrollBarsSeparatorBackground" Color="{StaticResource SystemChromeMediumColor}" Opacity="0.9"/>
<StaticResource x:Key="DataGridColumnHeaderForegroundBrush" ResourceKey="SystemControlForegroundBaseMediumBrush"/>
<StaticResource x:Key="DataGridColumnHeaderBackgroundColor" ResourceKey="SystemAltHighColor"/>
<SolidColorBrush x:Key="DataGridColumnHeaderBackgroundBrush" Color="Red"/>
<StaticResource x:Key="DataGridColumnHeaderHoveredBackgroundColor" ResourceKey="SystemListLowColor"/>
<StaticResource x:Key="DataGridColumnHeaderPressedBackgroundColor" ResourceKey="SystemListMediumColor"/>
<StaticResource x:Key="DataGridColumnHeaderDraggedBackgroundBrush" ResourceKey="SystemControlBackgroundChromeMediumLowBrush"/>
<StaticResource x:Key="DataGridColumnHeaderPointerOverBrush" ResourceKey="SystemControlHighlightListLowBrush"/>
<StaticResource x:Key="DataGridColumnHeaderPressedBrush" ResourceKey="SystemControlHighlightListMediumBrush"/>
</ResourceDictionary>
</ResourceDictionary.ThemeDictionaries>
<SolidColorBrush x:Key="SystemControlGridLinesBaseMediumLowBrush" Color="{StaticResource SystemBaseMediumLowColor}" Opacity="0.4"/>
<SolidColorBrush x:Key="SystemControlRowGroupHeaderBackgroundMediumBrush" Color="{StaticResource SystemChromeMediumColor}"/>
<SolidColorBrush x:Key="DataGridCurrencyVisualPrimaryBrush" Color="Transparent"/>
<StaticResource x:Key="DataGridColumnHeaderForegroundBrush" ResourceKey="SystemControlForegroundBaseMediumBrush"/>
<SolidColorBrush x:Key="DataGridColumnHeaderBackgroundColor" Color="Red"/>
<SolidColorBrush x:Key="DataGridColumnHeaderBackgroundBrush" Color="Red"/>
<StaticResource x:Key="DataGridColumnHeaderHoveredBackgroundColor" ResourceKey="SystemListLowColor"/>
<StaticResource x:Key="DataGridColumnHeaderPressedBackgroundColor" ResourceKey="SystemListMediumColor"/>
<x:String x:Key="SortIconAscending"></x:String>
<x:String x:Key="SortIconDescending"></x:String>
<StaticResource x:Key="GridLinesBrush" ResourceKey="SystemControlGridLinesBaseMediumLowBrush"/>
<StaticResource x:Key="DataGridCellFocusVisualPrimaryBrush" ResourceKey="SystemControlFocusVisualPrimaryBrush"/>
<StaticResource x:Key="DataGridCellFocusVisualSecondaryBrush" ResourceKey="SystemControlFocusVisualSecondaryBrush"/>
<Style x:Key="DataGridColumnHeaderNoSortStyle" TargetType="controlsprimitives:DataGridColumnHeader">
<Setter Property="Foreground" Value="{ThemeResource DataGridColumnHeaderForegroundBrush}"/>
<Setter Property="Background" Value="Blue"></Setter>
<Setter Property="HorizontalContentAlignment" Value="Stretch"/>
<Setter Property="VerticalContentAlignment" Value="Center"/>
<Setter Property="IsTabStop" Value="False"/>
<Setter Property="SeparatorBrush" Value="{ThemeResource GridLinesBrush}"/>
<Setter Property="Padding" Value="12,0,0,0"/>
<Setter Property="FontSize" Value="12"/>
<Setter Property="MinHeight" Value="32"/>
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="controlsprimitives:DataGridColumnHeader">
<Grid x:Name="ColumnHeaderRoot">
<Grid.ColumnDefinitions>
<ColumnDefinition Width="*"/>
<ColumnDefinition Width="Auto"/>
</Grid.ColumnDefinitions>
<VisualStateManager.VisualStateGroups>
<VisualStateGroup x:Name="CommonStates">
</VisualStateGroup>
<VisualStateGroup x:Name="FocusStates">
<VisualState x:Name="Unfocused"/>
<VisualState x:Name="Focused">
<Storyboard>
<DoubleAnimation Duration="0" Storyboard.TargetName="FocusVisual" Storyboard.TargetProperty="Opacity" To="1"/>
</Storyboard>
</VisualState>
</VisualStateGroup>
<VisualStateGroup x:Name="SortStates">
<VisualState x:Name="Unsorted"/>
<VisualState x:Name="SortAscending">
<Storyboard>
<DoubleAnimation Duration="0" Storyboard.TargetName="SortIcon" Storyboard.TargetProperty="Opacity" To="1"/>
</Storyboard>
</VisualState>
<VisualState x:Name="SortDescending">
<VisualState.Setters>
<Setter Target="SortIcon.Glyph" Value="{ThemeResource SortIconDescending}"/>
</VisualState.Setters>
<Storyboard>
<DoubleAnimation Duration="0" Storyboard.TargetName="SortIcon" Storyboard.TargetProperty="Opacity" To="1"/>
</Storyboard>
</VisualState>
</VisualStateGroup>
</VisualStateManager.VisualStateGroups>
<Rectangle x:Name="BackgroundRectangle" Grid.ColumnSpan="2" Fill="{TemplateBinding Background}" Stretch="Fill"/>
<Grid HorizontalAlignment="{TemplateBinding HorizontalContentAlignment}" Margin="{TemplateBinding Padding}" VerticalAlignment="{TemplateBinding VerticalContentAlignment}">
<Grid.ColumnDefinitions>
<ColumnDefinition Width="*"/>
<ColumnDefinition MinWidth="0" Width="Auto"/>
</Grid.ColumnDefinitions>
<ContentPresenter Content="{TemplateBinding Content}" HorizontalAlignment="Left" VerticalAlignment="Center"/>
<FontIcon x:Name="SortIcon" Grid.Column="1" FontFamily="{ThemeResource SymbolThemeFontFamily}" Foreground="{ThemeResource DataGridColumnHeaderForegroundBrush}" FontSize="12" Glyph="{ThemeResource SortIconAscending}" HorizontalAlignment="Center" Opacity="0" VerticalAlignment="Center"
Visibility="Collapsed"/>
</Grid>
<Rectangle x:Name="VerticalSeparator" Grid.Column="1" Fill="{TemplateBinding SeparatorBrush}" VerticalAlignment="Stretch" Visibility="{TemplateBinding SeparatorVisibility}" Width="1"/>
<Grid x:Name="FocusVisual" IsHitTestVisible="False" Opacity="0">
<Rectangle x:Name="FocusVisualPrimary" Fill="Transparent" HorizontalAlignment="Stretch" IsHitTestVisible="False" StrokeThickness="2" Stroke="{ThemeResource DataGridCellFocusVisualPrimaryBrush}" VerticalAlignment="Stretch"/>
<Rectangle x:Name="FocusVisualSecondary" Fill="Transparent" HorizontalAlignment="Stretch" IsHitTestVisible="False" Margin="2" StrokeThickness="1" Stroke="{ThemeResource DataGridCellFocusVisualSecondaryBrush}" VerticalAlignment="Stretch"/>
</Grid>
</Grid>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>
</ResourceDictionary>
</Page.Resources>
<controls:DataGrid x:Name="dataGrid1" ItemsSource="{x:Bind Customers}">
<controls:DataGrid.Columns>
<controls:DataGridTextColumn
Header="First Name"
Width="SizeToHeader"
Binding="{Binding FirstName}"
FontSize="20" HeaderStyle="{StaticResource MyDataGridColumnHeaderStyle}">
</controls:DataGridTextColumn>
</controls:DataGrid.Columns>
</controls:DataGrid>
Update:
If you want to override the DataGridColumnHeaderBackgroundColor, you can try the following method and don't need to change its default style.
.xaml:
<Page.Resources>
<Color x:Key="MyColumnHeaderBackgroundColor">Red</Color>
<StaticResource x:Key="DataGridColumnHeaderBackgroundColor" ResourceKey="MyColumnHeaderBackgroundColor"/>
</Page.Resources>