The settings of BirdieSync are not accessible in ActiveSync options, apart from chosing which category of items you want to synchronize. All the options should be accessed in Thunderbird or Sunbird in "Tools/BirdieSync options" menu. So clicking on the "Settings" button in ActiveSync option window doesn't produce any result.
By now, the synchronization only works both ways. But if you want to avoid synchronizing some contacts on the mobile (like messenger contacts), you should use contact category options to "exclude" some categories of contacts from synchronization. I suggest you to read BirdieSync help file to get more explanations about it. In this case, you'll very likely have to assign all your messenger contacts to a specific category that has no matching address book in Thunderbird, and therefore will not be synchronized.