I don't believe the Glazers would have a issue with any head coach/manager as long as said person has the credentials for the job imo. The Glazers wouldn't care less if Conte was appointed either and neither would the Glazers have to deal with him.
The people who would have major influence in who is brought in are the CEO and the three guys on the transfer committee (Bout, Lawlor, Court) and Murtough and Fletcher imo. And we need to remember that the aforementioned 5 have never been in a position of this much influence before when it comes to appointing a new head coach/manager. And it would be these people a new head coach will have to deal with and work with imo. And this relationship is the key to success if we want to challenge for major honours because streamlining the vision on how we want to play and hence recruit is the key to success and everybody needs to be on the same page or else things could go wrong very badly. So its important the guys heading the recruitment department select the new coach IMO.
We've spent a considerable amount of money in the last 6 - 7 years, revamping things at youth level, buying expensive youngsters, and putting in place mechanisms for the modern game. So the decision to appoint a new head coach/manager has to be a holistic one. John Murtough just last week was quoted as saying the following “Another element is style of play, an identity to what Manchester United is. We talk to players and coaches about playing fast, fluid attacking football, so when we link across all the age groups there’s a thread that runs through the football club.”
Who are the coaches who implement a fast fluid attacking brand of football and also bring through the talented youth at the top level (Champions League) whilst remaining competitive? I think we know the answer to that and it's the above criteria which has to be taken on board and the decision to hire a coach has to be based on the youth, identity as outlined by Murtough and having a rapport with the recruitment department IMO.