I don't have a problem with Alfred having a gun. It's something that's been shown in the past. He does have a military backstory as well. My problem lies with the fact that, to me, the picture is implying that he is a main player in Batman's crime fighting group in this show.
That kind of goes against the whole secret identity concept. Having Bruce's butler be involved on any kind of regular basis with Batman, is a huge connection that Bruce would not allow.