Per Martin Konicek's comment, to fully disable the selection of the items in the simplest manner:
<ListView>
<ListView.ItemContainerStyle>
<Style TargetType="ListViewItem">
<Setter Property="Focusable" Value="false"/>
</Style>
</ListView.ItemContainerStyle>
...
</ListView>
However if you still require the functionality of the ListView, like being able to select an item, then you can visually disable the styling of the selected item like so:
You can do this a number of ways, from changing the ListViewItem's ControlTemplate to just setting a style (much easier). You can create a style for the ListViewItems using the ItemContainerStyle and 'turn off' the background and border brush when it is selected.
<ListView>
<ListView.ItemContainerStyle>
<Style TargetType="{x:Type ListViewItem}">
<Style.Triggers>
<Trigger Property="IsSelected"
Value="True">
<Setter Property="Background"
Value="{x:Null}" />
<Setter Property="BorderBrush"
Value="{x:Null}" />
</Trigger>
</Style.Triggers>
</Style>
</ListView.ItemContainerStyle>
...
</ListView>
Also, unless you have some other way of notifying the user when the item is selected (or just for testing) you can add a column to represent the value:
<GridViewColumn Header="IsSelected"
DisplayMemberBinding="{Binding RelativeSource={RelativeSource Mode=FindAncestor, AncestorType={x:Type ListViewItem}}, Path=IsSelected}" />
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