One answer is to say that different elements came into the tale from an earlier mythological tradition but this suggests a tale-teller that wasn't in full control of the material. Whatever we think of Culhwch which is full of what might be regarded as scarcely integrated mythical material, the author of the Four Branches does seem to be writing stories in which the elements are consistently integrated. But the two identities of Rhiannon do not seem consistent. The final pages of Branwen eerily evoke something more otherwordly than the rest of the apparently Otherworld characters who come and go as ordinary people.
How can Rhiannon of the birds suddenly become Manawydan's wife? Could the author engage in a sort of double-think? We could propose that the sensibility of medieval authors was different from ours so that they could know what they were dealing with in terms of earlier mythical material while at the same time get on and present a story in the devout christian world they inhabited. Sometimes reading medieval literature I think this, but at others I think they were prone to an intense literalism and their faith was attached to material objects (like obviously fake holy relics). But perhaps they knew full well that they were fakes but nevertheless had faith in their efficacy.
We can learn to read the things they wrote, but can we ever read them as they wrote them?