I sincerely believe this whole issue comes from Oda wanting to "subvert expectations" on Kaido having a "son" who turned out to be female when introduced, but things went out of hand.
The problem here is obvious. We have an explicit statement from Yamato turning into a man because Oden was a man too (chapter 984). It's not like Yamato identified as a man and then added Oden's identity to his own (I will refer to him as masculine, for now, since that's his current self-definition). The problem, however, is Kaido and the Beast Pirates treating him as a man too, because I highly doubt his dad would happily accept Oden's impersonation and follow the masculine treatment from pretty much stealing his identity. He doesn't seem too progressive either.
I wouldn't be surprised this is a two side scenario: Kaido (and therefore his subordinates) refer to Yamato as a man because he wanted a son, not a daughter, as his successor. And Yamato assumed a masculine identity because of his obsession with Oden, as he explicitly explained. If this was the case it would be really funny as everything may lead to Yamato reassuring herself as that, Yamato, a woman, a daughter, not a man nor a son, the moment she doesn't need Oden anymore.
And let's make it clear, I would have no problem with Yamato being truly trans. But how he stated to call himself a man because Oden was so sounds fishy as hell and doesn't give the impression that he identified as a man before becoming Oden.