It's all agenda, but it's a normal mechanism from my point of view
Just look at how Yankers've been defending Big Meme until the very last even if she was the biggest disgrace ever to Yonko's hype.
They had to defend her, even if it was unwillingly
In the same way an Akainu fan would also defend the other admirals, even though maybe he doesn't really specifically care about them.
For the same agenda based mechanism all the Zoro haters will try to shit on the other swordsmen too, Mihawk and Ryuma especially.
It was a big surprise to me that anti Zoro pirates didn't downplay Oden, but I guess it's because they think that he's not tightly related to Zoro which at the end will backfire at them because the whole Enma blackening plot serves as a direct comparison between Zoro and Oden. It's only that they don't have realized it yet.
You can also see Sanji stans desperately trying to push the near equality between the number 2 and 3 of every organization.
Everything is agenda:
-A fan of a certain Yonko will defend other yonkos too, and shit on swordsmen because Mihawk is a legit threat
-Luffy fans: often allied with Yonko fandom because the Emperors are Luffy's direct enemies
-Zoro fans will defend all swordsmen and the vice captains
-Sanji fans will defend all the number 3s and shit on Mihawk because if Hawkeye is really Yonko level they can't dream anymore about Zoro >= Sanji since that even the most extremist of Sanji fans wouldn't argue about Sanji being Yonko level by EOS