A: After some discussion, we decided that Exchanging Keepers or Mixing Up everyone’s Keepers does not count as “Stealing” a Keeper.
Think of it this way: you cannot then reverse the action against your opponent. What would that mean? “…and instead you [Exchange] one of their Keepers”? “…and instead you [Mix Up] one of their Keepers”? Those doesn’t really make sense. So we concluded that Exchange or Mix It All Up are unstopped by It’s A Trap! Neither would you be able to use You Can’t Take This Guy From Me (a Surprise in Firefly Fluxx which has the same trigger as It’s A Trap).
What It’s A Trap! was designed to protect you against, in addition to Steal A Keeper, is any of those annoying other Keepers, like the Captain and the Scientist (who can steal certain Keepers at will. One of my favorite things is to put out a juicy Crew Member and wait for the person with the Captain to try to take it, at which point, instead… It’s A Trap! and I get to steal their Captain instead!
In Batman Fluxx, it was included for highly thematic reasons: Batman was always getting trapped by villains (at least in the live-action version), but Batman Fluxx includes a version of Plunder, called Crime Happens, which would be exactly the kind of thing which It’s a Trap! might also protect you from.