The deep ones are not worshipful, they acknowledge no gods. There are, however, those who they must respect. Mother Hydra, the great conglomeration, feeding tendrils groping upwards from Laurentian Abyss, grabbing some things and releasing others. Father Dagon, the giant, floating along the North Pacific Gyre, eating and growing and demanding more. Sister Echidna, which wanders the arctic, spitting monsters ashore. Brother Koshei, recently recovered from below Lake Baikal and held with caution and foolhardiness by the USSR. These are the subjects of deep one one art, the ones worthy of idolization.
Of course, words like "Father" and "Mother" are the result of a clumsy translation, as neither Dagon, Hydra, nor the deep ones have any sort of sex or gender. They are not family, but they are the closest thing.
The deep ones may have been human once. Ancient corpses, lost at sea, may have drifted into the clutches of an amorphous blob, a massively parallel genetic computer, and ancient meddler in natural history: a shoggoth. Once it had a sample of human DNA a shoggoth could have spent millenia "digesting" it, endlessly mixing and remixing it with all the sealife samples it had gathered before. If a viable combination were found, it would not be hard for the shoggoth to bud off an example of that creature, and release it into the sea.
But although the shoggoths made them, they are uncaring, and the deep ones have spent their whole lives immersed in the dream of Cthulhu.