I'm reading up on classic Greek theologies and cosmogonies (still in the stages of trawling through free online resources) and it seems to me that the Orphic reverence for Dionsysos threatens the position of other gods, in particular Zeus.
Was sectarian conflict an issue in Greek antiquity?
Are there any books you'd recommend for me on the topic?
There was virtually zero sectarian dissent in "Greek antiquity," which I'll take here to be the heyday of the Greeks, about the 8th to 3rd century BCE. The Orphic cult was one of several prominent mystery cults in existence, and one of the ones we know the least about. The most famous are the Eleusinian Mysteries, about which we know quite a bit, and the most notorious is the one which came later, the mystery cult of Christ. That one did not get along well with others, but that's in a Roman context, centuries later.
In Classical Athens, the Eleusinian Mystery cult and the "regular" or "traditionally Olympic" cults of the city existed side by side and were in fact closely integrated rather than at odds. Though Athens was definitely the city of Athena, Demeter and her daughter played a central role in the religious life of the city, not just at Eleusis but also in the festival of the Thesmophoria (famously brought to life in Aristophanes Thesmophoriadzusai). Dionysus was an important figure, especially at the theater, as was Pan. Mortal heroes like Theseus and Erechthios were also centrally important. Notice I have not even mentioned Zeus yet. He was present in the city, but by no means was primary. There was no sense of primacy, at least not for mortals, and there were no semi-divine accountants up in the sky measuring the volume of sacrificial smoke that rose up for one god versus another. It was Athena and Demeter and Dionysus at Athens; at Sparta it was Artemis; at Olympia, Zeus; at Delphi, Apollo; at Argos, Hera; at Ephesus, Artemis.
There is a kaleidoscope of good books on the topic. First, the basics:
Burkert, Walter, and John Raffan. 1985. Greek religion. Harvard University Press.
Ogden, Daniel. 2007. Companion to Greek religion. Blackwell.
Parker, Robert. 2011. On Greek religion. Cornell University Press.
Mikalson, Jon D. 2010. Ancient Greek religion. Wiley-Blackwell.
Kearns, Emily. 2010. Ancient Greek religion: a sourcebook. Wiley-Blackwell.
Buxton, R. G. A. 2000. Oxford readings in Greek religion.
Kindt, Julia. 2012. Rethinking Greek religion.
For Orpheus
The go-to used to be Guthrie, Orpheus and Greek Religion, but it is a little dated now. It is still fundamentally sound, but lacks some of the newer insights like what might be found in Graf and Johnston below.
Edmonds, Radcliffe G. 2013. Redefining Ancient Orphism: a Study in Greek Religion. Cambridge.
Gordon, R. L., and Marcel Detienne. 1981. Myth, religion, and society: structuralist essays. Cambridge University Press. [this is a French structuralist approach, obviously. see chapter 6 by Detienne, "the myth of 'honeyed Orpheus'".
Graf, Fritz, and Sarah Iles Johnston. 2013. Ritual texts for the afterlife: Orpheus and the Bacchic Gold Tablets. Routledge. [This is a great write-up of a specific Orphic object, with loads of references. When you see that blue Routledge cover, you know it is going to be rock-solid]
Betegh, Gábor. 2004. The Derveni papyrus: cosmology, theology, and interpretation. Cambridge.
Morand, Anne-France. 2001. Etudes sur les Hymnes orphiques. Brill.
Rudhardt, Jean, Philippe Borgeaud, Vinciane Pirenne-Delforge, Jean Rudhardt, and Jean Rudhardt. 2008. Opera inedita: Essai sur la religion grecque & Recherches sur les Hymnes orphiques. Liège: Centre international d'étude de la religion grecque antique.