I've been fascinated by fans, here and elsewhere, who are incensed by the idea of a Bruce/Barbara relationship.
Particularly the 'Killing Joke' adaptation controversy. Rabid anticipation for a story in which Barbara is shot, stripped, and then photographed turned to outrage because Batman and Batgirl have sex? Ummm, ok.
Just to lend some historical context, the Barbara Gordon Batgirl was intended to have a flirtatious back and forth with Batman since her conception. Created in 1966 in coordination with the 'Batman' tv series, show producer William Dozier "intended 'to develop a strong romantic interest working both ways between Batman and Batgirl'"(Batman: A Celebration, p.222). In her very first appearance ("Enter Batgirl, Exit Penguin"), it is also clear that her father, Commissioner Gordon, is trying to encourage a romantic pairing between recent college graduate Barbara and thirty-something Bruce Wayne. Not thought to be so outrageous, even in 1967.
I know that the favored romantic pairing by fandom now is Dick Grayson and Babs, but for years Robin (depicted as a few years younger than Batgirl in both the books and tv show) was portrayed as having a not very serious schoolboy crush on the more mature Batgirl.
In the Lego Batman movie, Dick Grayson/Robin is a kid, Bruce/Batman and Barbara/Batgirl are adults (well, at least chronologically, if not emotionally, in Bruce's case). A romance between the two characters makes sense and has historical precedent.
In fact, one could make a strong case that a Barbara Gordon/Batgirl-Bruce Wayne/Batman coupling makes more sense than any romantic pairing in Batman's long history (considering values, goals, even work schedules). Certainly more so than any civilian or even Catwoman.
Just some things to consider before virtually wretching at the appalling, horrifying thought of even a silly tease of a Batman/Batgirl romance.