In the latest movie, Justice League, I observed that on at least two occasions, Batman didn't care about his secret identity.
When he was beating the thug to lure out the parademon. Parademon just blows up and he, whilst talking to the criminal, calls for Alfred's help. Now, what if that crooked man deduced Batman's secret identity by narrowing down the poeple in Gotham who had a friend named "Alfred"?
When Bruce Wayne is with Arthur Curry and he calls Bruce "the Batman" in front of few of those people. It's highly likely that those people don't speak English, but what if someone knew who Batman was?
Later on in the movie, when Barry meets Diana for the first time and sees the bat-signal, he says that we need to go. But this is done in a way to not to reveal his secret identity (at least Barry thinks so, or maybe he feels silly because he was stating the obvious)?
My question is, why does Batman not care about his alter-ego Bruce Wayne going public (Bruce Wayne is the Batman, this might have serious repercussions)?
Follow up question: If yes (he doesn't care), why wear the mask at all? Is he under the cognitive dissonance?