Book-Stannis is obsessed with getting what's his by right. I always considered that his supreme defining character trait, aside from his unbending inflexibility. He's always grinding his teeth because he craves so hard for the power that he considers his by right. His craving for that power is stronger than any other thing going through his mind. Everything else comes second... his daughter, his wife, his brother, his familial traditions (Storm's End), friendship, love, and his superficial devotion to religion, they're all secondary to him.
The whole reason he turned to Mel in the first place was that his craving for power was bigger than his revulsion at her religion (and any religion in general). Despite Mel's impressive feats, I never got the impression that Book-Stannis turned into a real believer. He's always rude and impatient whenever she talks about visions and such... I think Rhollor is just a means to an end to him. Stannis never has or says anything indicating that he thinks about Rhollor as anything other than a device to be used to help Stannis get what's his. If Stannis got a letter from the High Septon, inviting him to come to King's Landing be hailed King on the condition that he returns to the faith, Book-Stannis would abandon Rhollor at once and command Selyse and the rest of his men to do as as well.
That's true. But the High Sparrow is also very stubborn. He has no respect for R'hllor, or Stannis for that matter. I doubt he would even invite Stannis to come to KL and become King. As it's shown in the quote provided by danm_999 (thank you danm_999 for the quote)
He nodded. “Last of all, and worst of all, there are some who say your children were not fathered by King Robert, that they are bastards born of incest and adultery.”
“Stannis says that,” Cersei said at once. “A lie, a lie, a palpable lie. Stannis wants the Iron Throne for himself, but his brother’s children stand in his way, so he must needs claim that they are not his brother’s. That filthy letter … there is no shred of truth to it. I deny it.”
The High Septon placed both hands flat upon the table and pushed himself to his feet. “Good. Lord Stannis has turned from the truth of the Seven to worship a red demon, and his false faith has no place in these Seven Kingdoms.”
That was almost reassuring. Cersei nodded. “Even so,” His High Holiness went on, “these are terrible charges, and the realm must know the truth of them. If Your Grace has told it true, no doubt a trial will prove your innocence.”
If it comes to that, the Tyrell men will storm Baelor's and throw the High Septon into a black cell. It might lead to rioting and mayhem in King's Landing but who cares, they're not going to tolerate such a turn of events. Mace Tyrells might as well head for the nearest dung heap and put a big load of shit on his head if he's willing to let a jumped up errant priest spit in his face.
Ah, but you forget that now the Faith is armed again, and like I said before, the High Sparrow is very stubborn and "just".