Do you think its possible to be an professed atheist in a setting where there are clerics running around? You don't reject the gods and you're not sitting on the fence - you outright don't believe they exist despite hard evidence to the contrary.
Well, it is important to define what this atheism is. It can be far more nuanced than, "that being you call a god does not exist".
You can walk up to a guy wearing a military uniform, and you can say, "I don't believe you are *actually* in the military" or you can say, "I don't believe you exist." The former is a far easier sell than the latter. Questioning outright existence is harder than questioning status and classification - you can see a powerful being, admit it physically exists, but deny its deific status.
Many modern Hindus follow just this idea - the beings of mythology exist, but they are just more beings, not "gods", often more flawed than humans, rather than objects of worship.
Also, note that many people say, "well, in D&D worlds there is *proof* of the gods!" I question that. People walking around casting spells is not proof the gods exist. It is proof that there is some source of power, but the "god" may be a human idea around which people frame use of the power. In a pseudo-Medieval world, unless the gods have personally and physically manifested within living memory, their existence can be reasonably questioned.
If so, what does that mean when you die? Does the carpet get pulled out from under you and you get allocated to a plane anyway? Or do the gods get all petulant and send you to the hells?
You are the GM. You decide the metaphysics of your world. There are many possibilities.
It is entirely possible for the gods to exist, but to not be involved in "the afterlife" - there are common real-world examples of this. Maybe your afterlife is determined by your actions, no matter what the gods think. Or, maybe the gods are involved, and they shuffle you to punishment for your temerity. Or maybe those who don't believe go to a separate afterlife. Or maybe there is some god or power that doesn't take worship that handles such cases.
Perhaps more importantly, you may need to decide where the cleric's power comes from. Is it that a deific entity is not required to be a cleric - powerful will is all that's necessary, or maybe it is hereditary, and the religions scoop up all the endowed peoples? Is it that there is a spiritual entity aligned with the cleric's ideas that grants power to the character? Is there a trickster god that's having a big joke? In a world with gods, why does this character have power?