namespace ListBoxTest
{
  public partial class MainWindow
  {
    public MainWindow()
    {
      InitializeComponent();
    }
  }

  public class MainModel
  {
    public MainModel()
    {
      Items = typeof(Type).GetProperties().Select(p => p.Name).ToList();
      var maxName = Items.OrderByDescending(n => n.Length).First();
      Console.WriteLine(maxName);
      var tb = new TextBlock();
      MaxItemWidth = new FormattedText(
        maxName,
        CultureInfo.CurrentCulture,
        FlowDirection.LeftToRight,
        new Typeface(tb.FontFamily, tb.FontStyle, tb.FontWeight, tb.FontStretch),
        tb.FontSize,
        Brushes.Black,
        new NumberSubstitution(),
        TextFormattingMode.Display
      ).Width + 16D;
    }
    public IReadOnlyCollection<string> Items { get; }
    public double MaxItemWidth { get; }
  }
}

<Window
  x:Class="ListBoxTest.MainWindow"
  xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
  xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
  xmlns:local="clr-namespace:ListBoxTest"
  Height="400"
  Width="600"
  WindowStartupLocation="CenterOwner">

  <Window.Resources>
    <local:MainModel x:Key="MainModel" />
    <DataTemplate x:Key="ItemsTemplate">
      <Border
        Margin="5"
        Width="{Binding Source={StaticResource MainModel}, Path=MaxItemWidth}"
        Height="{Binding Source={StaticResource MainModel}, Path=MaxItemWidth}"
        BorderThickness="1"
        BorderBrush="Gray"
        Background="Transparent">
        <TextBlock
          VerticalAlignment="Center"
          HorizontalAlignment="Center"
          Text="{Binding}"/>
      </Border>
    </DataTemplate>
  </Window.Resources>

  <Window.DataContext>
    <StaticResource ResourceKey="MainModel" />
  </Window.DataContext>

  <ListBox
    ItemsSource="{Binding Items}"
    SelectionMode="Single"
    ScrollViewer.HorizontalScrollBarVisibility="Disabled"
    ItemTemplate="{StaticResource ItemsTemplate}">
    <ListBox.ItemsPanel>
      <ItemsPanelTemplate>
        <WrapPanel IsItemsHost="True" Orientation="Horizontal"/>
      </ItemsPanelTemplate>
    </ListBox.ItemsPanel>
  </ListBox>
</Window>

<Window
  x:Class="ListBoxTest.MainWindow"
  xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
  xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
  xmlns:local="clr-namespace:ListBoxTest"
  Height="400"
  Width="600"
  WindowStartupLocation="CenterOwner">

  <Window.Resources>
    <local:MainModel x:Key="MainModel" />
    <DataTemplate x:Key="ItemsTemplate">
      <Grid>
        <Grid.ColumnDefinitions>
          <ColumnDefinition Width="Auto" SharedSizeGroup="CellGroup" />
        </Grid.ColumnDefinitions>
        <Grid.RowDefinitions>
          <RowDefinition Height="Auto" SharedSizeGroup="CellGroup" />
        </Grid.RowDefinitions>
        <Border
          Margin="5"
          BorderThickness="1"
          BorderBrush="Gray"
          Background="Transparent">
          <TextBlock
            Margin="5"
            VerticalAlignment="Center"
            HorizontalAlignment="Center"
            Text="{Binding}"/>
        </Border>
      </Grid>
    </DataTemplate>
  </Window.Resources>

  <Window.DataContext>
    <StaticResource ResourceKey="MainModel" />
  </Window.DataContext>

  <ListBox
    Grid.IsSharedSizeScope="True"
    ItemsSource="{Binding Items}"
    SelectionMode="Single"
    ScrollViewer.HorizontalScrollBarVisibility="Disabled"
    ItemTemplate="{StaticResource ItemsTemplate}">
    <ListBox.ItemsPanel>
      <ItemsPanelTemplate>
        <WrapPanel IsItemsHost="True" Orientation="Horizontal"/>
      </ItemsPanelTemplate>
    </ListBox.ItemsPanel>
  </ListBox>
</Window>

namespace ListBoxTest
{
  public class MyWrapPanel : WrapPanel
  {
    public MyWrapPanel()
    {
      Loaded += (s, ea) =>
      {
        var maxWidth = InternalChildren.OfType<FrameworkElement>().Max(e => e.ActualWidth);
        if (maxWidth > 0)
        {
          ItemWidth = maxWidth;
          ItemHeight = maxWidth;
        }
      };
    }
  }
}

<ListBox
  ItemsSource="{Binding Items}"
  SelectionMode="Single"
  ScrollViewer.HorizontalScrollBarVisibility="Disabled"
  HorizontalContentAlignment="Stretch"
  VerticalContentAlignment="Stretch"
  ItemTemplate="{StaticResource ItemsTemplate}">
  <ListBox.ItemsPanel>
    <ItemsPanelTemplate>
      <local:MyWrapPanel Orientation="Horizontal"/>
    </ItemsPanelTemplate>
  </ListBox.ItemsPanel>
</ListBox>