I can’t speak for Christian practice, but as for Conservative and Orthodox Jews, well, GOD or God functions as a proper noun, but is treated in Jewish Law (which includes prohibitions against erasing the name of God) as a Kinuy, which means “nickname”. It is a description (the hebrew word, Adonai, means something along the lines of “my Lord”, with lord pluralized for the sake of exaltation) of the deity who goes by the name of YHWH, which may not be pronounced under any circumstances and may only be written under certain circumstances. almost no circumstances allow destruction of a scroll with that name on it.
Kinuyim, though they are quite a step down from the actual name, are also treated with considerable respect, and are not pronounced in vain or written lightly. God and LORD, in an English translation, are translations that usually correspond to Elohim and YHWH, but neither is a name, and both serve as descriptions, and translated ones at that, and in the latter case, badly translated ones at that. The Eternal is also a fairly common translation of YHWH, which is probably a better one because the name shares a hebrew root with verbs that mean “to exist” (the same root as the “am” in “I am that I am, which is more accurately rendered I continue to be that which I continue to be”).
Translations of God’s nicknames, thus, are treated with a modicum of respect, though it is deemed unnecessary by most to hyphenate G-D. It has everything to do with respect for the deity and his name, the Tetragrammaton, which is not to be uttered, and nothing at all to do with bashing other deities or religions. They simply do not factor into the legal rulings concerning Hebrew (and later, translated) writing and pronouncing of the names and kinuyim of God.
As for capitalizing God vs. writing gods, well, a similar distinction manifests itself in Jewish law. I cannot vocalize “Elohim” when referring to God out of the context of prayer or Torah study. Were I to find myself needing to refer to Elohim, I would pronounce it “elokim”. however, if i were referring to pagan deities, I would say elohim (plural, not referring as the other Elohim does to one single being) because it is simply a word, not a name or ‘nickname’.
hope that was somewhat helpful.