The reality is that the disabled style of a DatePicker in WPF is difficult to read. You COULD restyle the whole freaking thing. Or you could do something simple, like just re-templating the control based on the IsEnabled property.
Like this:
<Window x:Class="WpfApplication1.MainWindow"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:sys="clr-namespace:System;assembly=mscorlib"
Title="MainWindow" Height="650" Width="550">
<Window.Resources>
<sys:DateTime x:Key="MyValue">1/1/2000</sys:DateTime>
<Style TargetType="{x:Type DatePicker}">
<Style.Triggers>
<Trigger Property="IsEnabled" Value="false">
<Setter Property="Template">
<Setter.Value>
<ControlTemplate>
<Border BorderBrush="Black" BorderThickness="1">
<TextBlock Text="{Binding Path=SelectedDate,
StringFormat={}{0:d},
RelativeSource={RelativeSource TemplatedParent}}"
VerticalAlignment="Center" HorizontalAlignment="Left"
Padding="4,0,0,0" />
</Border>
</ControlTemplate>
</Setter.Value>
</Setter>
</Trigger>
</Style.Triggers>
</Style>
</Window.Resources>
<DatePicker IsEnabled="False" SelectedDate="{StaticResource MyValue}"
Width="100" Height="25" />
</Window>