As an avid Tolkien fan and an increasingly active member of this site, I cannot count the number of times I've seen people refer to the Valar or Maiar as gods, only to be corrected by other members (often of high reputation) that they are more like angels, etc.
Even if the Maiar are more like angels (a Gabriel/Gandalf comparison has a lot of merit), the Valar are almost exactly gods, taken from Greek or Norse mythology with barely even any alteration. They have specialties and spheres of influence, they are supernatural beings of incredible power, they are immortal (at least to the extent that Greek deities are), they live in a magical land just like Asgard or Mt Olympus, they were involved with the creation and shaping of the world before retreating back after the coming of men, etc. Aule in Valinor is practically interchangeable with Hephaestus on Mt Olympus, Yavanna with Demeter, Ulmo with Poseidon, and on and on and on.
Obviously Eru Ilúvatar rules over them as the utmost power in Arda, but hierarchical relationships are well-known in polytheistic traditions. Tolkien himself was a Christian, and he famously kept Middle-earth from having too much religious flavor in-universe, but he must have known that a lot of his creations would have been heretical if they'd been presented as more than fiction (e.g. "God gave dominion over the Earth to men, not men and elves!" or "God required no input from his angels to create the world!"), so why would this particular distinction be so important?
Where does this tradition of the Valar being absolutely, positively not considered gods come from? Did Tolkien himself insist on it? If so, did he ever comment on why he patterned them so clearly off of a polytheistic tradition (i.e. specialized nature-deities with their own kingdom, desires, and familial relationships), rather than a more monotheistic structure (i.e. angelic spirits of goodness without independent lives, serving as messengers of a single authority)?