Two battles have embroiled Bob Iger ever since he returned to Walt Disney Co. for his second stint as CEO — one against activist investor Nelson Peltz’s Trian Partners LP, and the other against the perception that Disney is a “woke” company pushing a left-leaning agenda.

Iger now has a decisive win against Trian, keeping Peltz and his ally, former Disney Chief Financial Officer Jay Rasulo, off the board, and he’s earned the right to celebrate that victory. But when it come to that second fight, he might be chalking up a W prematurely.

On Thursday, Iger told CNBC that he thought Disney was out of the woods on the culture wars — that the noise around the issue has “sort of quieted down.”