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Apatheism (a highly original portmanteau of "apathy" and "theism") is an attiude that the very question of whether or not deities exist is not relevant or meaningful in life. Apatheists are not even interested in addressing any claims for or against god(s). Almost literally "I don't care about gods." It's not a claim, belief or belief system but an attitude.
Author and journalist Jonathan Rauch quite effectively described apatheism as:
[A] disinclination to care all that much about one's own religion and even a stronger disinclination to care about other people's.
Criticism of the idea
A criticism of the idea of Apatheism is that the assumption of "any gods existing or not is irrelevant to life" only works in the event that any existing deities are essentially non-interventionist - A deistic god has little relevance to the world while the Greco-Roman pantheon (known in mythology for meting retribution for the slightest of perceived insults) being real would have several real-world implications, as would many other religions' mythological figures.