Because they probably believed, like many people in the 1960s, that rock was a subversive genre of music and that the soldiers fighting in Vietnam would become subversive or insubordinate if they listened to it. Cronauer, who had a history of angering superiors, decided to ignore that rule because he felt that, things being as tense as they were during the war, the soldiers needed some sort of release from the death, destruction, and general tension felt throughout their ranks. Cronauer's use of humor was also frowned upon as being subversive.

Sergeant Major Dickerson and Lieutenant Hauk are both obviously by-the-book soldiers BUT, their orders to prevent rock music playing on the air likely came from higher up in the chain of command so the two both felt that the letter of the law needed to be followed. Also, it's pretty clear that at least Hauk didn't like rock music himself & therefore we can assume that, given his domineering personality, Dickerson didn't like it either.

Yes. More info can be found on him here, although the article is quite short. The film takes great liberties with the story, as films like this often do.