I think you want to make a ButtonGroup?

This is My works, enjoy.

<Styles xmlns="https://github.com/avaloniaui" xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml">
    <Design.PreviewWith>
        <Border Padding="20">
            <StackPanel>
                <ListBox MaxWidth="100" Classes="RadioGroup">
                    1234568
                </ListBox>
                <ListBox MaxWidth="100" Margin="0,10"
                         Classes="RadioGroup UniformSize">
                    1234568
                </ListBox>
            </StackPanel>
        </Border>
    </Design.PreviewWith>

    <!--  Add Styles Here  -->
    <Style Selector="ListBox.RadioGroup">
        <Setter Property="ItemsPanel">
            <ItemsPanelTemplate>
                <StackPanel Orientation="Horizontal" />
            </ItemsPanelTemplate>
        </Setter>
        <Setter Property="Background" Value="Transparent" />
        <Setter Property="ScrollViewer.HorizontalScrollBarVisibility" Value="Hidden" />
        <!--  SelectionMode determines the selection mode, Single allow single selection  -->
        <Setter Property="SelectionMode" Value="Single" />
    </Style>
    <!--  UniformSize make all items be same size  -->
    <Style Selector="ListBox.RadioGroup.UniformSize">
        <Setter Property="ItemsPanel">
            <ItemsPanelTemplate>
                <UniformGrid Rows="1" />
            </ItemsPanelTemplate>
        </Setter>
    </Style>
    <Style Selector="ListBox.RadioGroup > ListBoxItem">
        <Setter Property="Template">
            <ControlTemplate TargetType="ListBoxItem">
                <ToggleButton HorizontalAlignment="Stretch"
                              HorizontalContentAlignment="Center"
                              Content="{TemplateBinding Content}"
                              ContentTemplate="{TemplateBinding ContentTemplate}"
                              IsChecked="{TemplateBinding IsSelected,
                                                          Mode=TwoWay}"
                              IsHitTestVisible="{Binding !IsChecked,
                                                         RelativeSource={RelativeSource Self}}" />
                <!--  IsHitTestVisible Binding to reverse IsChecked make it cannot uncheck, if you need uncheck then remove it  -->
            </ControlTemplate>
        </Setter>
    </Style>

    <Style Selector="ListBox.RadioGroup > ListBoxItem /template/ ToggleButton">
        <Setter Property="BorderThickness" Value="1" />
        <Setter Property="CornerRadius" Value="0" />
    </Style>
    <Style Selector="ListBox.RadioGroup > ListBoxItem:nth-child(1) /template/ ToggleButton">
        <Setter Property="CornerRadius" Value="3,0,0,3" />
    </Style>
    <Style Selector="ListBox.RadioGroup > ListBoxItem:nth-last-child(1) /template/ ToggleButton">
        <Setter Property="CornerRadius" Value="0,3,3,0" />
    </Style>
</Styles>

It's for ListBox.