A lot of hints and implications can be found among the public statements or in the absence of them, but at the end it is all up for reader's interpretation.
There is the fact that Oda and Kubo never adress each other in the magazine Table of Contents comment section, not even on occasion of marriage or publication anniversary. They do so plenty for other mangaka.
Also, there is this Switch magazine interview from 2009:
-So the dignity you carry as a boy’s comic author Oda-san, is it safe to say that was something you’d already set in stone from when you started One Piece?
Yeah I think so. Because I mean, I approached it thinking that since I’m drawing for a boys’ comic magazine, then it’s my job to make sure they enjoy what they’re reading. When you actually do become a professional you’ll start getting fan letters and other things and you’ll soon find that the overwhelming majority of them are from girls. Boys just aren’t the type to pick up a pen*. (laughs) They don’t have things like stationary or stamps and they don’t think about going through the ‘grueling task’ of writing someone just to say, “That was cool.” Boys are a life form that enjoy something but won’t bother to tell you that they actually do.
So I learned that girls will flood you with their opinions and when I took at step back and looked at the world of manga, I realized that there are a lot of people out there that made me think, “This [author] is really just going along with the girls’ opinions.” And ultimately, if you’re considering those opinions as the ‘needs of the customer’ when you write the story, you’re just left with a girl’s manga. (laughs) It’s like, if you do that, you’re only writing to entertain girls, and that’s just wrong.
A direct statement which could have been adressed at certain author, half of the magazine, or a good part of the industry.
Not exactly conclusive evidence.
For a different example, 2009 Liar Game/Invitation databook interview between Kaitani and Oda had this little interesting bit:
Kaitani- The good thing about 'mangaka' is that there's no rank amongst us. Of course there are popular and not-so-popular ones but when you become a professional, we all do our best with our abilities in our individual works.
Oda- In that case actually I'm the complete opposite. I want a degree of rank amongst us. I'm working this hard so I really wonder why some other people can hold the same title of 'mangaka'.
Again, a statement that was not adressed to anyone in particular. But after this interview was published, the internet was uniformly claiming Oda had a certain Togashi Yoshihiro in mind.
Oda is a popular author who is known to make bold statements from time to time which inevitably brings this kind of speculation. But is more fascinating to see who he is friends with rather than enemies, since these kinds of relationships may give us exciting collaborations and tribute art.