although Bruce's civilian ID is a bit faked I don't think he's so much about deception. In fact I think Batman kind of forces honesty from his opponents, because well if they aren't bad guys they have nothing to fear from Batman.
Bruce has faith in the entire Batclan, meanwhile the standards he holds his fellow heroes to are so ridiculously high he must have some degree of faith in them
And the sexism is only in bad writing. Take a look at how he treated Batgirl in that Bronze Age story posted yesterday. Sure it was ages ago, but really if stories where the major female characters in Batman comics were good writing they wouldn't be consistently retconned.