While it is true that belief in religion tends to be described as binary (whether it really is or not), things like generic pantheism and animism actually do exist separately from religion, and neither obligates worship or an absolutist position on the existence of a deity. Is it still a "God" if you don't worship it?
If something's being called a god solely because it's worshipped, or even if the worship is the tipping point, it probably isn't going to meet the more commonly accepted criteria of what constitutes a "god" with respect to theism and atheism. Of course, if that's even coming into play, definitions will fairly certainly need to be compared to keep things clear. "Money is a merchant's god," for example, is not employing a definition of "god" that applies to theism or atheism.
Well... that's where things get a little blurry. As far as I'm concerned, the whole damn question is nothing but word salad once you have enough discipline to ignore irrelevant traditions.
While it's true that one can generally break terms like theist and atheist apart from their common usage and down into greater and greater levels of specificity, that doesn't mean that the common usage isn't useful for common purposes.
Also, what of the person that leans theistic on Wednesdays and atheistic on Mondays -- what label should we attach to those? One oddity about humans is that they tend to be inconsistent.
Theist on Wednesdays and atheist on Mondays, perhaps, dependent on what more specific criteria are actually in play for the usage? Was there anyone who claimed that the beliefs of a person are immutable, unchangeable, or that atheist and theist were terms that were proscriptive instead of descriptive? One could note that it's generally not as arbitrary or mutable as you're suggesting, so using the term for a state that is represented significantly more during a representative period of time is generally within reasonable usage, too.
When the question itself is wrong, there can be no coherent answers.
True enough, though potentially inaccurate as a statement, depending on what, exactly, is "wrong." However, your objections here don't seem to actually demonstrate that this question is actually wrong, but rather that an excessively simple understanding of the concepts in play that shouldn't be in play is wrong.
