Probably the most notable example of such is Sayim Ghafadar from the fiction line who is an Inquisitor of Pharasma, one of the Boneyard's most effective troubleshooters, and an atheist.
There are probably a lot of those.
The Gods of PF don't speak with their worshippers often enough to guarantee a single official interpretation of their dogma... Which is good.
At the end of the day, a Church is but an organization made of people, with all that entails. Dissensions, politics, internal power struggles theological disagreements, fanatcism, of various breeds, schisms...
If the church of Sarenrae, of all things, is on the brink of implosion, we know mortals still have their free will and both the means and the will to abuse it and make bad decisions on their own, as is tradition.
Plus more than a few of the clerics (not to even mention other believers) exist outside if the clerical structures entirely.
Which, by the way, only goes to prove further more the superiority of the Living God, praise be He.
One church, one voice, one mafia. All Hail Razmir.
I've played a character like this for years: a Chaotic Neutral Cleric of Lamashtu. He has become my go-to character, and was a favorite PC in my old group. He turned to Lamashtu in desperation after being disfigured in a fire set by a group of rivals, rather than being born a "freak" and reveling in it. He goes out of his way to help the disfigured and insane, teaching them they can become strong by enduring their nightmares. Strength and inner beauty through adversity and outer ugliness was his philosophy. And he once became the proud and doting father of a litter of half-fiend jackalweres.
Not a priest by games rules, but one of my favorite religious characters was an ugly, scarred mercenary from Molthune who worshiped Shelyn.
After spending years butchering people for money, he just said "to hell with it" and meandered off to find a Shelynite temple to pledge himself to. He just wanted to contribute to beauty after a life that had been nothing but ugly up to that point.
And he was awful at art, lousy with music, all of that. He was just this big ugly guard dog who hated doing what he was best at because what he was best at was converting live people into dead people. He just loved beauty.
He eventually took up gardening- he wasn't great at it, but gardening rewards diligence and care, which he was capable of lavishing on the plants he tried to rear. This ugly, scarred dude hanging out in the gardens around the temple, who occasionally has to go get his sword and armor out of storage to make the inadvisability of screwing with Shelyn's faithful or the communities they work with abundantly clear.
He's become my go-to for midlevel pickup one-off games.
Don't forget the ever chipper Laori Vaus. Zon Kuthon's sunniest cleric.