You don’t bind a command to the Click property. The Click property is for adding a traditional event handler to the Click event. You want to use the Command property to bind your command.
<Button Content="{Binding BackgroundMessage}"
HorizontalAlignment="Left" Width="75"
VerticalAlignment="Top" Height="Auto" Margin="2"
Command="{Binding ElementName=MainGrid,
Path=DataContext.AlertClickCommand}"
CommandParameter="{Binding}" />