I've downloaded Gun Bros from the Market and can verify that Facebook does pop up as the game starts, and it tries to sync data all throughout gameplay. There's actually good reason for this, as it helps people who constantly wipe their phones or have multiple devices from starting over (I played on my Xperia Play, then popped it up on my Xoom and input my Facebook info- it picked right up where I left off, overwriting the Xooms old save file with the new one).
I recommend either uninstalling it and trying again or trying the above Airplane mode option. I don't know why it'd be freezing if you can't sync though.