Seems like a no brainer to me. To me, the point of consumer boycotts is to achieve a specific goal and not just to "punish bad companies" in some general sense. The latter is fine too, but it's difficult initiate, maintain, and quantify. Here we have a national chain store which a lot of people choose to shop at as an alternative to a certain other unpopular national chain store, and it's engaging in a very specific and very indefensible behavior.
Boycott Target.
