I use the word tathata to refer to the just-so-suchness, in which and of which I also inextricably am (including my consciousness); the just-so-suchness experienced in simple being-aware, before adding anything: e.g., thoughts and concepts. (The Buddhist term “empty mind” does not mean empty of perception.)
Because tathata is pre-/non-conceptual (including all “I-concepts” ), any words that I use (including these) can be no more than “fingers pointing to the moon.” Tathata itself is ineffable, and that word itself is just a label.
I sometimes use Brahman (or other words, such as Tao, or even Tathata if the context does not render that confusing) to refer to the Whole: the totality without an edge, the one-without-a-second, the all-without-another—of which we also are. The Whole itself has no proper analogy; it is not a figure that has a ground: it is the ground from which all figures arise, subsist, and pass away. I conclude to non-dualism from the non-separability and mutuality (Zen talk: “all things mutually arising” ) apparent in lived experience, particularly in non-thinking just-being-aware. (Fingers, again, metaphors and allusions...)
If someone uses the word “god” to mean much the same thing, then we understand one another, and we can talk from there, sorting out the details, sharing our varied metaphors. However, if someone else insists that “god” (a) entails a supernatural category,* and (b) necessarily refers to a supernatural individual—then we are not talking about the same thing at all. At that point, all discussion is likely to focus on dualism versus non-dualism, or on a supernatural spirituality versus (as Starrman put it) a natural spirituality.
The word “god” is simply a label: either for the non-conceptual ineffable, or for some conceptual complex. If I say that I “believe in the god (or the goddess)”, to what am I referring? As darthmix points out, what someone else thinks I am referring to is likely to depend on their particular “set of cultural traditions and associations and definitions.” In the RHP culture here, for example, it is likely to be generally taken as referring to supernatural theism; and rejection of the term “god” is likely to be taken as rejection of that supernatural theism. [Note just in this thread how the personal pronoun keeps cropping up.]
The potential for confusion expands when one realizes that some strictly non-supernaturalist, non-dualist spiritualities use theistic language (perhaps because it was inherited), but in a strictly metaphorical sense (e.g., Kashmiri Shaivism; some Advaita Vedantists, Sufis, Kabbalists, etc.).
I have no intrinsic objection to the word; I simply do not use it in this “culture”—and if I do, I am careful define what I mean by it; or, more specifically, what I do not mean. I am not sure exactly what one is abandoning by simply abandoning the word.
* By “supernatural” here, I mean extra-natural, or extra-cosmic, not simply beyond our comprehension. I do not assume that there are no aspects of the natural cosmos that transcend the “grammar of our consciousness”; and I do not take Brahman to be supernatural.