次にここに来る人のために、テンプレートを次のように設定することでこの問題を解決しました。
<Style TargetType="{x:Type ContextMenu}">
<Setter Property="Background" Value="{StaticResource ShadeBrush}" />
<Setter Property="BorderBrush" Value="{StaticResource ShadeBrush}" />
<Setter Property="Foreground" Value="White" />
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="{x:Type ContextMenu}">
<Border Uid="Border_93">
<Border.Style>
<Style TargetType="{x:Type Border}">
<Setter Property="Tag"
Value="{DynamicResource
{x:Static SystemParameters.DropShadowKey}}"/>
<Style.Triggers>
<DataTrigger
Binding="{Binding Tag,
RelativeSource={RelativeSource Self}}"
Value="True">
<Setter Property="Background"
Value="Transparent"/>
<Setter Property="Padding"
Value="0,0,5,5"/>
<Setter Property="Effect">
<Setter.Value>
<DropShadowEffect
BlurRadius="4"
Opacity="0.8"
ShadowDepth="1"/>
</Setter.Value>
</Setter>
</DataTrigger>
</Style.Triggers>
</Style>
</Border.Style>
<Border BorderBrush="{TemplateBinding BorderBrush}"
BorderThickness="{TemplateBinding BorderThickness}"
Background="{TemplateBinding Background}"
Uid="Border_50">
<ScrollViewer CanContentScroll="True"
Style="{DynamicResource {ComponentResourceKey ResourceId=MenuScrollViewer,
TypeInTargetAssembly={x:Type FrameworkElement}}}"
Uid="ScrollViewer_9">
<ItemsPresenter
KeyboardNavigation.DirectionalNavigation="Cycle"
Margin="{TemplateBinding Padding}"
SnapsToDevicePixels="{TemplateBinding SnapsToDevicePixels}"
Uid="ItemsPresenter_5"/>
</ScrollViewer>
</Border>
</Border>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>