I have some evidence that complicates things, and points to a possiblity that Philodemus held different views than Epicurus did.
I found this on Wikipedia, which seems to indicate that Epicurus held similar views on the Gods to Theodorus.
QuoteTheodorus was attacked for atheism. "He did away with all opinions respecting the Gods," says Laërtius,[17] but some critics doubt whether he was absolutely an atheist, or simply denied the existence of the deities of popular belief. The charge of atheism is sustained by the popular designation of Atheus, by the authority of Cicero,[18] Laërtius,[2] Pseudo-Plutarch,[19] Sextus Empiricus,[20] and some Christian writers; while some others (e.g. Clement of Alexandria)[21] speak of him as only rejecting the popular theology.
Theodorus wrote a book called On the Gods (Περὶ Θεῶν). Laërtius had seen it, and said that it was not to be dismissed,[17] adding that it was said to have been the source of many of the statements or arguments of Epicurus.