She was persuading Tommen to send her back to Casterly Rock....That's what led to Cersei into having the Sparrows legitimized.
You really wanted them to waste time showing Margery and Cersei snipping at each other??? They've been doing that since the beginning of season 3. Lady Oleynna went back home, why would she rush back to Kings Landing just cuz Margery is 'snipping' with Cersei? How would they even use the Sparrows when they had no power? Even if they did get Tommen to sign a decree, Cersei would subvert it immediately just because it was the Tyrrell's who made it happen. Cersei was acting as de facto ruler, she wouldn't let them legitimize the Sparrows. (Never mind the fact that before they were legitimized, they weren't even on the radar of the royalty, so how would Lady Olynena even know about them?)
I don't see what's so unbelievable about the cult. They have told you that before Aegon conquered Westeros, the Faith Militant was an armed group that carried out the justice of the gods and no one was exempt, not even kings and queens. The Targs threw them in the bushes cuz they're crazy, Cersei brought them back because she is dumb and thought she could use them to take out the Tyrrell's. This re-legitimization is made possible because the King is so weak.