Meaning of "she will never get sore" in 1950s

As Bill Franke and Jon Hanna tell you, sore means “angry” here, in the sense of “upset” or “vexed” rather than “enraged”. But when The Music Man came out this use was already on the wane (note that the play is set in 1912). It was regarded in the 50s as slang of our parents’ generation, and now is rarely used in any but the physical sense of “ache-y”; in the sense at hand it was replaced by “pissed” or, for a while, “bent out of shape”.

It was not always slang in this sense. The earliest instance of “sore at” in COHA occurs in Henry Adams’ novel Democracy, where a character of the social elite uses the phrase in a serious conversation about politics:

  “What, then, is the danger you fear?”
  “That he will offend all the important party leaders in order to conciliate unimportant ones, perhaps sentimental ones, like your friend French; that he will make foolish appointments without taking advice. By the way, have you seen French to-day?”
  “No, " replied Madeleine; “I think he must be sore at your treatment of him last evening. You were very rude to him.”
  “Not a bit,” said Ratcliffe; “these reformers need it. His attack on me was meant for a challenge. I saw it in his manner.”

And sore has never (until now) been reserved for bodily pain: “sore at heart”, “sore disappointment”, “sore repentance” have been clichés for hundreds of years. Cynewulf’s Crist applies it to sorȝceare, “grieving anxiety” about the year 900.

You may or may not have had the misfortune to fall into an argument with your date on the way to dinner, or another event, leaving both of you sore in the sense of angry or upset.

If nothing else, it's surely bad for one's digestion.

The lyric promises that its subject will never do so.