Their established characters are they do what is best for business, which gives them the freedom to float back and forth depending on the story and segment. They're really above true heel or face labels except when they need to be, much like Brock and Taker. They back Rollins because Rollins is a champion who they can control, which they feel is best for business. Stephanie backs the Divas Revolution because it is best for business. They book Seth in matches against Cena and Sting because, while having a champion they control is best for business, they can't deny putting on money matches because...it is best for business.
Their character motivations have been explained basically every week for 2 years now. Everything they do is consistent with the characters they've portrayed.
Except their "best for business" line was supposed to be a heel line, where they would hold down the babyface people wanted (Bryan) in favour of their own corporate champion (Orton). It was supposed to be a meta angle playing off of WWE's real preferences for what stars are "supposed" to look like. They were absolutely meant to be heels, constantly screwing over the faces and propping up their stable members.
Somewhere after WM 30, they started to forget whether they were meant to be heels or not and started hovering back and forth. Yet they are still the Authority, backing the heel WWE champion, only they keep switching nonsensically between being heel and face, usually on the same show. Stephanie is a heel while with Seth, then switches to being a face with the Divas revolution.
I mean, remember when they did everything to make Rollins champion (including cheating to help him win MITB) and wanted Brock gone in favour of Rollins, doing all they can to stack the deck for Rollins? Then suddenly a few months later they themselves bring Brock back to trounce Rollins, their own guy, apparently to "test" Rollins or something. There's no consistent motivation, they are blank slates for whatever the story is supposed to be. So how can anyone give a shit about what they do, or get invested?