Was "the right stuff" ever really the right stuff?
Well, kind of,

The technical portrayal of test pilots in that film received negative reviews with real test pilots.  I know Chuck Yeager did not like his portrayal by Sam Shepherd and director Philip Kaufman, particularly with the NF-104 accident at the end of the film.  While the scene is based on a real accident which Yeager did have, it was part of a scheduled test flight with established test points and not Yeager throwing on a pressure suit and jumping into the cockpit for a joyride with a YOLO type attitude.

Flight test and test pilot work is rigorously planned out, methodically didacted and cogitated, with multiple contingency plans and contingency plans for those if they don’t work.  Long gone are the days where you strapped your little pink fanny into a crate, pushed it off a cliff, and hoped for the best on the way down.  Test pilots and flight test engineers are very bright and methodical people who are intimately familiar with the systems of the aircraft they are flight testing and have spent a great deal of time thinking about all the ways something can go wrong and what they intend to do if they encounter this problem.  Hundreds, if not thousands of hours have been spent in systems and and flight simulation scenarios, not only evaluating these hypotheses, but making detailed plans for their test points they want to evaluate during flight.  Finally the flight testing itself is a slow and methodical affair, slowly and carefully increasing the performance envelope with each flight and thoroughly evaluating and addressing anomalies once encountered before continuing.  As one test pilot once put it, “We try to make flight testing as boring as possible.”

As to being cool, calm, unflappable under pressure, quick thinking and courageous being the defining qualities of 'the right stuff' in a pilot.  I would argue that they ARE useful to a pilot anywhere.  Remember US Airways Flight 1549's Capt Chesley 'Sully' Sullenberger?  That guy was faced with one of the most challenging scenarios out there and was a cool as a refrigerated cucumber throughout.  You may not be exploring and mapping out the absolute edges of an F-35's flight envelope, but those skills can come in handy with any kind of emergency situation which you might face.

Remember there is a difference between these qualities and having hazardous attitudes e.g. anti-authority, machismo, etc.  As Yeager once put it "If you want to grow old as a pilot, you gotta know when to push it and when to back off."  In addition flight test is a considerably different animal than it was back in Yeager's day, thanks in part to Yeager and a few unfortunates who now have a street at Edwards named after them.

Test flying isn't about being taking big risks; its a gradual and methodical process of exploring the flight characteristics of an aircraft and having multiple contingency plans to make it as safe as possible.  In short, good Aeronautical Decision Making really IS 'The Right Stuff'.  Risk takers, the macho guys, or the just plain stupid get weeded out, either by their superiors or by Natural Selection.