How to trigger DataTemplateSelector when property changes?

As you requested an example with datatriggers in the comments, here you are:

A FrameworkElement can only have EventTriggers, therefore you get the error Message Triggers collection members must be of type EventTrigger

And also don't use a ContentPresenter directly, it is meant to be used inside a ControlTemplate. Better use a ContentControl when you want to have dynamic content.See What's the difference between ContentControl and ContentPresenter?

And finally here's a suggestion to your DataTrigger issue. I have put it inside a style for reusability ....

XAML :

<Window x:Class="WpfApplication88.MainWindow"        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"        Title="MainWindow" Height="350" Width="525">  <Window.Resources>    <DataTemplate x:Key="requiredTemplate">      <TextBlock Text="requiredTemplate"></TextBlock>      <!--your stuff here-->    </DataTemplate>    <DataTemplate x:Key="completedTemplate">      <TextBlock Text="CompletedTemplate"></TextBlock>      <!--your stuff here-->    </DataTemplate>    <Style x:Key="selectableContentStyle" TargetType="{x:Type ContentControl}">      <Style.Triggers>        <DataTrigger Binding="{Binding Path=CurrentStatus}" Value="Required">          <Setter Property="ContentTemplate" Value="{StaticResource requiredTemplate}" />        </DataTrigger>        <DataTrigger Binding="{Binding Path=CurrentStatus}" Value="Completed">          <Setter Property="ContentTemplate" Value="{StaticResource completedTemplate}" />        </DataTrigger>        <!--  your other Status' here -->      </Style.Triggers>    </Style>  </Window.Resources>  <Grid>    <ContentControl Width="100" Height="100" Style="{StaticResource selectableContentStyle}"/>  </Grid></Window>

I could be wrong, but I believe the DataTemplateSelector is only used when the ItemContainerGenerator creates a container for an item added to the collection. Because a new container isn't generated when a property value changes, a new DataTemplate is never going to be applied via the selector.

As suggested in the comments, I would recommend you look at the VisualStateManager or data triggers, otherwise you're going to have to recreate the container for every item when one or more properties change value.

Just as an extra choice - if you want to stick to your templates, just use s binding with converter.