There's a few ways this could be done. If you look at the Precedence List on the MSDN
then you can see that the Forground set in ways 1-8 will override the Foreground from a default style. The easiest way being just to set the local value in the TextBox.
<TextBox Foreground="Red" />
Another thing that you can do is use the 'BasedOn' property of styles to override the other versions. This does require giving a key value to your default style, but that can then be used to also apply the default like in this example:
<Style TargetType="{x:Type TextBox}"
x:Key="myTextBoxStyle">
<Setter Property="Foreground"
Value="Red" />
<Setter Property="FontWeight"
Value="Bold" />
</Style>
<!-- Style applies to all TextBoxes -->
<Style TargetType="{x:Type TextBox}"
BasedOn="{StaticResource myTextBoxStyle}" />
<TextBox Text="Hello">
<TextBox.Style>
<Style BasedOn="{StaticResource myTextBoxStyle}" TargetType="{x:Type TextBox}">
<Setter Property="Foreground"
Value="Blue" />
</Style>
</TextBox.Style>
</TextBox>
Edit:
In the case that the default style is applying a value and you want to revert it to the base value there are a few ways I can think of, off hand, to get this behavior. You can't, that I know of, bind back to the default theme value in a generic manner.
We can however do some other things. If we need the style to not apply some properties, we can set the style to {x:Null}, thus stopping the default style from applying. Or we can give the element it's own style that does not inherit from the base style and then re-apply only the setters that we need:
<TextBox Text="Hello" Style="{x:Null}" />
<TextBox Text="Hello">
<TextBox.Style>
<Style TargetType="{x:Type TextBox}">
<Setter Property="FontWeight"
Value="Bold" />
</Style>
</TextBox.Style>
</TextBox>
We could modify the default style so that the Foreground will only be set on certain conditions, such as the Tag being a certain value.
<Style TargetType="{x:Type TextBox}"
x:Key="myTextBoxStyle">
<Setter Property="FontWeight"
Value="Bold" />
<Style.Triggers>
<Trigger Property="Tag"
Value="ApplyForeground">
<Setter Property="Foreground"
Value="Red" />
</Trigger>
</Style.Triggers>
</Style>
<TextBox Text="Hello" />
<TextBox Text="Hello" Tag="ApplyForeground" />