Are NACA airfoils used in modern aircraft design?
Just three data points: The tail surfaces of the Pilatus PC-12 still use the venerable NACA 0012, even though a better alternative (from the Wortmann FX 71 L series) was proposed. It did not help that the Wortmann airfoil is used on many small airplanes, has more lift and less drag and an abundance of data exists on it: The (mainly British) engineers at Pilatus were too conservative to use anything newer than an airfoil from the 1920s.



Pilatus PC-12 (picture source).

The wing of the Dornier Seastar, designed by a group of old Dornier engineers in the early 1980s, used the same airfoils as the venerable Do-17 of the 1930s, namely the NACA 23012. Later flight tests showed the need to add a leading edge droop on the outer wing, a modification that cost several knots in top speed and would have been entirely avoidable with better airfoils and/or the use of washout.



Dornier Seastar. Picture by Rschider (own work).

The excellent Polish aerobatic glider Swift S-1 uses indeed a NACA 6-digit airfoil, the $64_1412$. As Jerzy Makula explained to me, it gives excellent snap roll and spin control, and when flying the prototype, I could control the exit direction from a spin within ±15° with very little practice. Jerzy simply took what had worked before.



Swift S-1. Picture by TSRL (own work).

Generally, small companies or experimental airplane builders still rely sometimes on the NACA series, but in general better alternatives exist. Big companies use custom-made airfoils, helped by computer codes which model not only the two-dimensional flow around the isolated airfoil, but can optimize the specific wing section by including the influence of engine nacelles, pylons and the fuselage. Well-designed wing roots do not use one single airfoil, but a three-dimensional shape which minimizes interference drag.

This is true even for glider companies. While Wolf Lemke used his own creations for the early LS series of gliders on the basis of their good looks (and with good success), todays gliders are designed in the computer, helped by university departments which relish the chance to let students work on real-world designs.