You're mostly correct that the turn of the millenium was a big pivot in philosophy in that sense. The religions back then were the regional polytheistic pagan faiths, and if you were a philosopher that wanted to talk phil. of religion, you either commentated on developings there or developed a heretical metaphysical system. Most schools in early and mid-antiquity Greece did the latter. Platonism developed the idea of the One which would largely be adopted by monotheism in the future. Aristotle in the Metaphysics made the case for an Unmoved Mover that was "pure actuality" to be later adopted by Thomas Aquinas in the Middle Ages. Many schools like Stoicism and Cynicism developed pantheistic ideas of a "World Soul", which also overlapped with Platonism.

After Christianity gained traction in late antiquity (last few centuries of the Roman Empire), both among common folk and the emperors who started to become hostile towards Roman paganism and shutting down temples/destroying "idols", Hellenic pagan philosophers started to come out of the shadows and defend the native faith that was until those days taken for granted. The biggest trend there was in Neoplatonism. Proclus took Plotinus's earlier quasi-monotheism and bent it back towards polytheism in his Elements of Theology, and others like Olympiodorus followed suit in developing polytheist metaphysics and hermeneutics. See Edward Butler's Essays on a Polytheistic Philosophy of Religion.

Shifting back to the early classical era, in the East, the famous Laozi/Confucius/Siddhartha Gautama each took Asia in new directions. Sometimes they develope ideas of what westerners would call "deities" like the Tao, but they were more focused on ethics and embedded their systems in the local polytheist folk-religions.