apatheism
n.— «I think you’ll find that the stance of simply not caring much about God or religion (“apatheism” in the jokey parlance) is much less common than you imagine. It seems to be growing as people get wealthier, but a depressingly predominate chunk of humanity believes that God is indeed worth caring about, one way or another.» —“Cut God Some Slack” by dgriffith Freakonomics Blog Aug. 2, 2007. (source: Double-Tongued Dictionary)
Further reading
Have you ever googled your own name and found someone else who goes by the very same moniker? There’s a word for that: googleganger. Plus, the language of hobbyists and enthusiasts: If you’re a beekeeper, perhaps you call yourself a...
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You cite an etymological Note: apa(th)y + -theism.
I submit that a equally valid origin might be ap + atheism.