Among them was General Curtis LeMay who IIRC smoked cigars and was reported to make sure that he sat next to Taylor in meetings knowing that Taylor hated tobacco smoke.
If you want to read about Taylor, Lemay and the Joint Chiefs leading up to our decisions to get more involved in Vietnam, read Dereliction of Duty by H. McMaster. A great book about how that idiot McNamara and Johnson manipulated and divided the JCS to get what it wanted in the runup to Vietnam. BTW, as pointed out in the book, Lemay and the Marine Commandant (Wallace Green) were of the same mind. Bomb North Vietnam back into the stone age or get out of Vietnam all together. No half stepping.
You will also find out in the book that Lemay’s tour as chief of the Air Force was extended a year not because Johnson liked him. But because he was afraid Lemay as a civilian would be criticizing Johnson concerning Vietnam while Johnson was running for the 1964 Presidential election. Lemay as a good military man would never criticize his commander in chief while in uniform.