WPF dynamic layout: how to enforce square proportions (width equals height)?

Try this – it seems to work in Kaxaml:

<Button 
    MinWidth="{Binding ActualHeight, RelativeSource={RelativeSource Self}}" 
    MinHeight="{Binding ActualWidth, RelativeSource={RelativeSource Self}}">
  Some content
</Button>

(To test, I put a TextBox inside the button, because that’s an easy way to change content size without re-parsing the Xaml.)

Edit: sorry, should probably have specified it as a style to match your example:

<Style TargetType="Button" x:Key="SquareButton">
  <Setter Property="MinWidth" Value="{Binding ActualHeight, RelativeSource={RelativeSource Self}}" />
  <Setter Property="MinHeight" Value="{Binding ActualWidth, RelativeSource={RelativeSource Self}}" />
</Style>