Neither do I. I'll take the risk of doing a real-world analogy, which can be touchy when speaking of religion, but being an atheist, I think there is no god. When I say that, I imply "in our universe". If, when the bing bang started, another bubble universe was created at the same time, with which we cannot interact (and which can't interact with our universe), and a godlike being took charge of "his" universe, my real-life worldview wouldn't be invalidated, because its existence would be improvable and be functionnaly meaningless in our reality.
For an Eberron denizen, FR worlds and the rest of the multiverse is as unknowable as other bubble universes are to our universe. And while most people in Breland would be convinced of the existence of Aureon and pray to Dol Dorn before a battle, a few atheist could postulate that these gods don't exist based on lack of scientific evidence.They wouldn't have an opinion whether there are parallel universes (such as the one close off by the ring of Syberis) exists, if they have a population and if there are gods there (because they have no way to prove it).
Besides, I am not sure FR gods would be considered gods by said Eberron denizen : if these gods found there way to Eberron (which is canonically impossible), they would be powerless cripples, not something anyone would liken to a god. Meeting Pelor or Lathander or Corellon in a bar in Sharn wouldn't even prove the existence of the gods from an Eberonnian point of view.