Polytheology: Syncretism, Process Theology, and "Polyamorotheism"
These types of syncretism, which arise when cultures come into contact and effectively "new" deities emerge from the mix, is an example of what the Christian theologian Alfred North Whitehead called "process theology." This view of theology is, actually, quite in accord with evolution, and argues against ideas like predestination and determinism. Process theology suggests that deities change just as much as humans do, and that we all meet the continuously unfolding wave-front of creative existence on the same footing, as it were.
The gods are evolving, developing, and becoming just as much as we are. Osiris, Dionysos, and Jupiter never knew they had as much in common until a bunch of Greeks (and later Romans) started to worship Serapis. Then aspects of these various individual deities emerged as a further individual deity, which did not replace any of the individuals, but instead proliferated on his own (though sometimes in close connection or in concert with these other divine beings). The gods are not unchangeable and eternal in their being, they are dynamic and expanding, just as equally as humans are, in this process theological view. The syncretism of ages past is yet another way of understanding process theology; the concept was working equally well twenty centuries back, even though the name would not come about until relatively recently. It is not a "sign of degeneracy" in a culture to have flourishing syncretism, it is a sign of its vitality.
The type of syncretism in which one deity is identified with another, further, does not necessarily negate this. Modern neoplatonic scholar/philosopher Edward Butler has explained this phenomenon as "polycentric polytheism." This encompasses (and in many ways surpasses) both the concepts of "hard polytheism" and "soft polytheism" by the idea that any deity can be any other deity in that particular deity's particular manner. So, Persephone-Ereshkigal would be Persephone acting in the role or manner of Ereshkigal, but in a definitely Persephone fashion. The same role in a play as interpreted by two different actors is an analogous concept: Guinness' Obi-Wan Kenobi is different than McGregor's Obi-Wan Kenobi, for example.
If each ritual or act of devotion -- represented by ancient religious texts and inscriptions or by any festival or spiritual observance of modern Pagans -- can be understood as a performance, then this sort of syncretism can continue to occur: if two deities can be invited to participate, great, but sometimes one deity may be doing so in the role of another. This is theoretically possible for any two deities -- Loki and Coyote could end up playing each other, for example -- and by understanding things in this way, issues of cultural appropriation can be defused. The utmost respect should be observed at all times in calling upon and attempting to honor the deities of another culture. No one should present themselves as "authentically" practicing any tradition in which they have not been properly and officially trained (especially if it is not one's own familiar culture); this level of integrity is definitely within human hands, and depends on human consistency and honesty.
And yet, who is to say that the gods that respond (if and when they do) are not actually deities with whom individuals are already familiar from their other practices, who have simply adopted these other roles? It takes a great deal of discernment to determine what is going on in situations like this, but it is a process that has occurred for a very long time. We should give the benefit of the doubt to both the gods and to the people of the past who produced devotional works for the gods in situations where these types of hitherto unknown syncretism occurred. Likewise, we should not be averse to the possibility that these kinds of syncretism can still occur in the future, given the larger mix of populations and intermingling cultures that we are experiencing in the modern world.