Theological syncretism takes many forms in a variety of cultures.  It can include such things as the fusing of two (or more) different deities in Egyptian or Graeco-Egyptian culture, as is the case with Amun-Re, Re-Harakhte, Sobek-Re, Zeus-Ammon, Hermanubis, Bawy (Set and Horus combined), and Pataikos/Ptah-Sokar-Osiris, for example.  It can involve the subsuming of many deities into the overarching folds of one deity, as is the case with Isis and many goddesses from Egyptian, Greek, Near Eastern, and other cultures.  It can involve the identities, names, attributes, or epithets of one deity being adopted by another in particular localized forms, as is the case with Jupiter Optimus Maximus Dolichenus (who was, in any case, worshipped far outside of the sphere of Roman Asia Minor!).
 
But, no matter how many distinct or indistinct types of theological syncretism occur, and no matter how wide an array of examples can be cited, one matter does tend to hold sway in almost every culture where it is found:  theological syncretistic combinations tend to occur amongst deities of the same gender.   While it is tempting to suggest, therefore, that syncretism can be a way to imagine polyamorotheism allowing deities of the same gender to produce (syncretized) offspring, the prevalence of this pattern instead prompts me at present to observe that the impermeability of the boundaries various cultures have observed between the binary genders is something noteworthy.  For all of the gender-variance that can and does occur with some deities in some pantheons, the majority do not seem to partake in such transgressions of the norms (insofar as any premodern culture has a concept of normativity—see Karma Lochrie’s Heterosyncrasies for more on this topic) of gender.
 
While my knowledge of all world mythologies and polytheistic cultures is quite limited, I can think of only five definite examples of syncretism which involve deity-forms that originate out of not only separate deities, but deities of different genders.  The final result of such combinations is not always a being that is non-binary gendered, either.  I will also discuss a further example that some might cite as favoring the multi-gender syncretism approach, but which on further and deeper reflection does not involve this at all; and finally, I will suggest some possibilities for the future as well.
 
I can think of two examples—both from Indian/Hindu mythology—where a new deity-form comes into existence and is accompanied by a narrative explaining how this came to be, and both of them involve the god Shiva.  In one, Shiva and Parvati are enjoying a bout of lovemaking, and become so enthralled with one another that they decide to fuse into one, and thus become Ardhnarishvara.  That hypostasis persists as its own deity afterwards, not unlike many other deities in Hinduism who originate as an avatar, aspect, or alternate (often utilitarian) form of deities that already existed.  Another instance of a fused male-and-female deity in Hinduism is Harihara, who originates in the love which Shiva had for Vishnu in Vishnu’s feminine form, Mohini, which results in the fusion of Shiva and Mohini.  Shiva also takes feminine form on some occasions—by choice or otherwise!—but these feminine forms do not tend to persist as discrete entities the way that Mohini appears to have done in relation to Vishnu.
 
I can also think of two East Asian deities that are the result of multi-gender theological syncretism, but no accompanying narrative or myth indicates how this took place; it was much more of a historical and, in the first case, a methodological syncretistic development (i.e. the result of several different religious systems comingling) than one which takes place on a mytho-theological level.  The first of these, Guanyin (also sometimes written as Kwan Yin), is a Chinese goddess in  traditional Chinese polytheism and Taoism, and is a bodhisattva in Buddhism, with variations in name and local languages throughout several East Asian cultures.  Her name is a Chinese translation of the name of the Sanskrit Avolakiteshvara, “the lord who looks down [to hear the cries of the suffering],” and in the original Chinese Mahayana Buddhist writings, Guanyin does appear as male and simply as a translation of the Sanskrit name.  As time goes on, an androgynous or feminine form becomes more common for Guanyin, and eventually the feminine form prevailed.  The feminine form and attributes, as well as many of the mythological accounts of her, certainly derive from indigenous Chinese polytheist sources rather than from Buddhist traditions about the bodhisattva.
 
The second deity—widely acknowledged as a “composite” deity, though the names and number of identities of the composition vary greatly—is the Shinto Inari-Okami, one of the most popular and widely-venerated kami, with over 32,000 shrines of the 80,000+ known shrines in Japan being devoted to this particular divine being.  Inari-Okami is known to appear in male, female, and androgynous forms of varying ages, as well as in the form of foxes (particularly white foxes), snakes, dragons, and on one occasion, a spider.  Inari-Okami is usually understood to be a singular entity, but on occasion, Inari-Okami is considered to be Inari-Sanza (“three-part” Inari) or Inari-Goza (“five-part” Inari).  The various other kami who might be identified with Inari-Okami, or with the constituent parts of this three- or five-part versions, include Ukanomitama, Ogetsu-Hime, Toyouke, Izanagi-Okami, Izanami-Okami, Ninigi, Wakumusubi, Ukemochi, Omiyanome, Tanaka, Shi, and Sarutahiko-no-Okami, or (in the specifically female form) the Buddhist Daikiniten or Benzaiten of the Seven Lucky Gods.  Very interestingly, Inari-Okami’s shrines are the only ones that are “official” but are, yet, not maintained by the Jinja Honcho that oversees all other Shinto activities in Japan (and elsewhere), but instead are maintained by everyday laypeople.  That such variation is observed in Inari-Okami’s worship, down to the level of gender, may thus be a reflection of this grassroots and individualized, localized, and community-specific veneration of the kami.
 
We have briefly examined two examples of multi-gender syncretism with mythological narratives of the etiology of such forms in Hinduism; we have also examined historical methodological syncretism leading to new deity-forms that span several gender categories in Chinese and Japanese polytheistic religions.  What about situations in which a fusion occurs between separate deities of different genders, but which has little historical context and no grounding in mythological narrative?  This is precisely what we have in the example of Hermekate, a fusion of (the male) Hermes and (the female) Hekate, attested in the lines of the Greek Magical Papyri (PGM) III, lines 45-47:  “I call upon you, Mother of all men, you who have brought together the limbs of Meliouchos, even Meliouchos himself, OROBASTRIA NEBOUTOSOUALETH, Entrapper, Mistress of corpses, Hermes, Hekate, […], Hermekate, LETH AMOUMAMOUTERMYOR…”  Based on the notes to the text, this name “Hermekate” may also occur in a few other defixiones, but I have not been able to confirm this at present.  In any case, what we have here is a magical formula, and such magical contexts are fertile grounds for novel syncretistic formations.  Though the formula before Hermekate’s appearance seems to indicate a feminine divinity is being addressed, clearly the combination of Hermes and Hekate, intended by the spell-writer to be in the mind of the one who reads it and uses it since the individual forms are given beforehand, complicates the picture of the “Mother of all men” and “Mistress of corpses” considerably.  Hermes and Hekate are perhaps a “natural match,” in any case, due to their similar functions and associations, though their mythology does not often overlap.  Also, given the Graeco-Egyptian context, double theophoric names (e.g. Sarapammon, Hermantinous, etc.) are also not uncommon, so even if a permanent multi-gendered syncretism was not intended, nonetheless the combination of the powers of both deities on this occasion were drawn upon in a manner that would have not been unusual, despite the unexpected divine gender mixing.
 
One ambiguous divine figure (and the ambiguity is in the divine status, not the gender) that many might consider as an example of multi-gender syncretism in the Greek world is Hermaphroditos.  The origins of a possible cultus to Hermaphroditos may date back to a Cyprian form of Aphrodite that was portrayed as bearded, and thus was called Aphroditos, which dates at least back to the 7th century BCE.  The philosopher Theophrastus writes of Hermaphroditos in the 3rd century BCE, and both Diodorus Siculus and Ovid write of this figure in the 1st century BCE, with only Ovid giving the story of the male child of Hermes and Aphrodite becoming fused with the nymph Salmacis into the multi-gendered form familiar from ancient depictions of a breasted, feminine-like figure with male genitals.  Hermaphroditos is also discussed by Macrobius as late as the 5th century CE.  Whether Hermaphroditos was ever worshipped as a full deity, or only as a particular form of Cyprian Aphrodite, is not as clear, and thus their situation is quite ambiguous on a theological level.  But, additionally, Hermaphroditos is never portrayed, under that name, as a theological syncretistic fusion of Hermes and Aphrodite, but instead as the child of the two deities, which is quite different than most of the multi-gendered syncretistic examples we have discussed here.
 
Based on these various examples, it is obvious that while not by any means common, such multi-gendered syncretisms could be possible.  Edward Butler, in “Polycentric Polytheism and the Philosophy of Religion“ (available here), argues that every deity, by virtue of being a deity, has the potential to embody or act in the role of any other deity, and in arguing this, he makes no caveats on the gender of the deities involved.  Given that this is the case, it is perhaps strange that such multi-gendered syncretisms are not more common than the few examples given here, and the likely limited number of others out there as well.  (If I have missed any, please inform me of them in the comments below!  I’m always happy to learn more in this area!)
 
It may be, to an extent, inherent in Egyptian tradition already, since the various “Eye of Re” goddesses (e.g. Hathor, Sekhmet, Tefnut, Wadjet, Mehit, Sia, Bast, Qadesh, etc.) are, obviously, feminine in comparison to Re himself, and thus are often considered to be his daughters; though perhaps an interpretation whereby they are not only instantiations of Re’s power, but instead are multi-gendered syncretisms of Re with various goddesses, would be beneficial.  The possibility of multi-gendered Greek syncretisms also seems intriguing and potentially revelatory, especially in the context of magic and the historiolae (short mythic narratives) that accompany and empower magical utterances and operations.  Would it be possible, for example, for a syncretism of Hermes and Persephone—Persephermes?—to assist mystery initiates in returning from the underworld with the blessings of its queen but the guidance of the psychopomp?  It seems possible, but then again, anything is possible where deities are concerned.