While the predominant religion in Westeros has always been that of The Seven, Game of Thrones has always reminded us of the alternatives. Those in the North, especially the Starks, keep faith with the Old Gods. Some hold with both the Old Gods and the New.
Then there are the Red Priests and Red Priestesses. These worshippers of R'hllor were originally from Essos. (Thoros is from Myr, Melisandre is from Asshai.) But characters from Westeros have also been drawn into their beliefs, whether it be Stannis and his wife, Beric Dondarrion, or even Davos Seaworth for a few minutes at the beginning of Season 6 when he convinced Melisandre to bring Jon Snow back.
The Hound, on the other hand, is one of those who dismisses all these religious beliefs out of hand. He doesn't believe in the bloody gods, any more than he believes in those who rule Westeros giving damn about anybody but themselves.
Though the show cut most of Sansa's practicing of piety to the Old Gods while she's stuck in King's Landing, it's one of those thing The Hound sneers at her for, even as he crushes on her. While traveling with Arya, we see him behave in godless fashion towards everyone he meets, including the man who he mugged on their way out of town in Season 4. And though Arya left him for dead, and now The Hound is alive, when Brother Ray, who was supposedly responsible for this miracle, begins holding forth on religion, The Hound dismisses him out of hand.
It's interesting that The Hound's trip back to the very home where he mugged that (now deceased) father and daughter is where he had his first religious vision.
Characters peer into the flames all the time in A Song of Ice and Fire. But only those who worship R'hllor ever see anything other than the firelight. That is, until last night. So how come The Hound is having visions?
One theory posits that The Hound has been favored by R'hollr ever since his childhood when he was forced into a fire by his older brother, the Now-Undead-Mountain. It's just that his terror of the flames stemming from that trauma has kept him from ever looking into one up until now. That's certainly an interesting theory, and would make The Hound an unknowing Red Priest.
But another suggestion, and one I like a whole lot more, is that this gift of The Hound's is brand spanking new. He only received the ability to look into the flames and see visions of the present and the future in the past few months -- when he died after Arya left him and then was brought back to life by R'hllor, only to be found and taken in by Brother Ray.
I like this theory because a resurrected Hound is actually a thing book readers believe they see when Brienne passes through the Quiet Isle. The Elder Brother tells her The Hound died in his arms, but the hooded gravedigger seems to be suspiciously Hound-esque, causing fans to wonder if two Undead Cleganes roam Westeros, destined to fight one day.
It seemed last year, the Hound returning, uncloaked, and clearly alive was the TV show abandoning this plot line. But with this newfound ability to see into the flames (and interpret his visions better than Melisandre), could they be hinting that instead if The Hound asking Beric "Why you?," he should really be asking, "Why me?"