Not defending Gutekunst - at all - but he does hold the cards, at least for now. Rodgers is under contract until 2023, so they don't have to do anything. And if Rodgers decides to be pissy and hold out, or sit, it's not going to be a good look for him.
I'm betting they find a way to work it out. The whole thing looks like it was staged - announcing it on the eve of the draft? How dramatic!
And of course then Gutekunst picks a defensive player in the first round. Guess you gotta do your job, after all.