private void updateBindng(FrameworkElement fe, DependencyProperty dp)
{
fe.GetBindingExpression(dp)?.UpdateTarget();
}

private void update()
{
this.updateBinding(this.textbox, TextBox.TextProperty);
this.updateBinding(this.label, Label.ContentProperty);
}

<StackPanel>
<Label x:Name="label">
<Label.Style>
<Style TargetType="Label">
<Style.Triggers>
<DataTrigger Binding="{Binding flag}" Value="True">
<Setter Property="Content" Value="flag is true"/>
</DataTrigger>
<DataTrigger Binding="{Binding flag}" Value="False">
<Setter Property="Content" Value="flag is false"/>
</DataTrigger>
</Style.Triggers>
</Style>
</Label.Style>
</Label>
<Button Click="Button_Click1">TOGGLE</Button>
<Button Click="Button_Click2">UPDATE</Button>
</StackPanel>

public partial class Window1 : Window
{
public Window1()
{
InitializeComponent();
this.DataContext = new Windows1Data();
}

private void Button_Click1(object sender, RoutedEventArgs e)
{
var data = (this.DataContext as Windows1Data);
data.flag = !data.flag;
}

private void Button_Click2(object sender, RoutedEventArgs e)
{
var sh = Type.GetType("System.Windows.StyleHelper, PresentationFramework, Version = 4.0.0.0, Culture = neutral, PublicKeyToken = 31bf3856ad364e35");
var sdf = sh.GetField("StyleDataField", BindingFlags.Static | BindingFlags.NonPublic).GetValue(null);
var ensureInstanceData = sh.GetMethods(BindingFlags.Static | BindingFlags.NonPublic).First(m =>
{
return m.Name == "EnsureInstanceData" && m.GetParameters().Length == 3;
});
var label_values = ensureInstanceData.Invoke(null, new object[] { sdf, this.label, 0 }) as IDictionary;

foreach (var trigger in this.label.Style.Triggers)
{
if(trigger is DataTrigger data_trigger)
{
var binding_expression = label_values[data_trigger.Binding] as BindingExpressionBase;
binding_expression.UpdateTarget();
}
}
}
}

public class Windows1Data
{
public bool flag { get; set; } = false;
}