Pretty much all the advertising (and other media content) at CL games is determined by UEFA and clubs have no say in the matter. If a club has big screens and wants to use them, it has to toe the line. It’s just an extension of the oversized pitch side advertising hoardings that have been in place at CL games since before the screens became commonplace.
Unfortunately there’s just too much dosh involved for clubs to rebel and not do what the evil UEFA paymasters dictate. And even if a club did decide to take a stand, not complying would no doubt have dramatic consequences.