The Glazers do not understand football. They have no sense of the tribalism that comes with it. Their NFL franchise could move from Tampa and end up across the country in Santa Fe. That's normal for them. The attachment and regionalism that accompanies English (and European) football is alien to them. The embarrassment that will come if Rodgers leads Man Utd to defeat at Anfield, and the Kop starts singing about 'Agent Brendan,' won't even have occurred to them.
Honestly, if we appoint Rodgers I'll actually feel sorry for him. In his first press conference the media will ask him if he thinks he can win over the United fans given his Liverpool history. From there the pressure will just grow. Solskjaer has had his taste of the ABU media. However, for the most part he's been shielded because he's a club legend. The media knows that there will always be a large contingent of fans who, even now, will never get nasty about Ole. So they don't lean into him as much as they could. That won't be the case with Rodgers. Whenever there's a bad result they'll be on him and the Liverpool fans will too. Playing it up, bantering United fans. Unless he comes in and goes on an insane winning streak he'll be eaten alive by the media.
I keep seeing people talk about Busby. When Busby became United manager players were still being transferred directly between United and Liverpool. The rivalry had not grown to the point its at now. You can't just magic away decades of the rivalry getting deeper, more intense and less civilised. Are people going to suddenly forget Liverpool fans trying to turn over Alan Smith's ambulance or something, just cos the rivalry wasn't as fierce in the 40s?