Affleck, a die-hard Red Sox fan, told Fincher he would simply not wear the hat, something that led to a small argument, reported the New York Times.
"I said, 'David, I love you, I would do anything for you,'" Affleck, 42, said.
"'But I will not wear a Yankees hat. I just can't. I can't wear it because it's going to become a thing, David. I will never hear the end of it. I can't do it.' And I couldn't put it on my head."
"That was the only fight David and I had and it was a legitimate fight."
More From This Section
Fincher said "it was like it's foregone, it's destiny" but Affleck stood his ground.
"It was an uprising; it was a coup, I rioted. It was a one-man riot against the Yankees."
After some "shuttle diplomacy, so much back-and-forth," the actor ended up wearing a Mets hat.
"This was very Switzerland," Affleck said of the compromise.