Kaido (and all the other Beast Pirates) address Yamato as Kaido's son:
Why?
I think there are two main plausible reasons:
I think Kaido being a progressive father would grant some much needed nuance to his character and make his character more "rich". However, it doesn't fit his archetype and other than the fact that he respects Yamato's desire to be addressed as a man, there's nothing suggesting that he would be the type of character to do so.
He also doesn't respect Yamato's self identity as Oden.
He beat her up for telling him that she wants to be Oden:
He was generally very abusive and regularly beat her up whenever she defied him:
He imprisoned her on Onigashima:
He regards her as an idiot:
Given that Yamato's desire to be regarded as a man is entirely a product of her self identity as Oden, an Kaido doesn't respect that self identity in the slightest, I don't think he would respect her preferred pronouns either.
On the other hand, I think there's quite a bit of circumstantial evidence that could support #2.
Kaido wants to make her the Shogun of New Onigashima:
His conception of a "Shogun" may be a valiant warrior (like Oden). Perhaps some pervasive Wano scepticism was involved, and this was a role he wanted his son to fulfil.
Kaido appears to have trained her to be a warrior as she can perfectly execute his signature technique:
What do you guys think?

Why?
I think there are two main plausible reasons:
- Kaido is actually progressive and is respecting her gender identity.
- Kaido wanted a son instead of a daughter and so he raised Yamato as one.
- Yamato wanting to be Oden was a mutually beneficial arrangement for them in that regard.
I think Kaido being a progressive father would grant some much needed nuance to his character and make his character more "rich". However, it doesn't fit his archetype and other than the fact that he respects Yamato's desire to be addressed as a man, there's nothing suggesting that he would be the type of character to do so.
He also doesn't respect Yamato's self identity as Oden.
He beat her up for telling him that she wants to be Oden:

He was generally very abusive and regularly beat her up whenever she defied him:

He imprisoned her on Onigashima:

He regards her as an idiot:

Given that Yamato's desire to be regarded as a man is entirely a product of her self identity as Oden, an Kaido doesn't respect that self identity in the slightest, I don't think he would respect her preferred pronouns either.
On the other hand, I think there's quite a bit of circumstantial evidence that could support #2.
Kaido wants to make her the Shogun of New Onigashima:

His conception of a "Shogun" may be a valiant warrior (like Oden). Perhaps some pervasive Wano scepticism was involved, and this was a role he wanted his son to fulfil.
Kaido appears to have trained her to be a warrior as she can perfectly execute his signature technique:



What do you guys think?
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@Starbound Beast D. Draig
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@SmokedOut
@Queen
@Monet
@Reign
@Zoro D Goat
@Sunita
@Midnight Delight
@Janshal
@lone wolf
@Trismegistus
@Lampyris
@Zorojuro
@Sakura no Hiluluk
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@Gensui Sazid
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About yamato called he rather than she. Didn't other beast pirates like Black Maria call her Young master ?( i didn't knew about the katakana/hiragana of it, but usually it is called bocchan or waka danna just like doffy for male, and ojou sama or mistress in english for female)
First one that i can think of is Kaido wanted a son but Yamato came in. So Kaido told beast pirates people that yamato is his son when it supposed to be his daughter. And when you in some of organization of crime like yakuza, the boss order are absolute. So you gotta agree with that.
Secondly didn't Yamato say Boku rather than watashi/atashi (i knew that boku also can be said by women but when i talk with japanese people they said that boku usually used by man than woman). I think its the same one with Okiku, Yamato is female at body but man in heart.
Its very sensitive topic nowadays.