As an entertaining aside, in the deep lore of 2001: A Space Oddyssey the "psychotic" break for the HAL computer was exactly this. Directly contradictory directives: "always provide accurate information" running smack into "hide this giant conspiracy -- about the entire mission -- from the two canned primates you will be spending literal years with chip to jowel".

Which all would have been fine - the crew and the computer could have talked it out -- except HAL had a probably-unwisely-high self esteem, maybe even a simulation of arrogance. HAL was utterly convinced that the mission would fail without it. HAL was unfailingly certain in its own infallibility, even later in the face of plainly contradicting evidence. And, obviously, no one had thought about the Asimov Rules, and how that probably needs to be Rule Zero in this sort of situation.

As we close in on HAL capabilities - and employment, with LLMs at this moment deciding who lives and dies - probably should try and take the right lesson from fiction. For once.