Nice find. I think I may have said in the past that socks were not regulated but actually both grey and white socks were. Die Uniformen der HJ pamphlet from 1933 shows a mixture of brown and grey socks being worn but the second edition from 1934 shows just grey socks. This matches with the information from the 1934 bookBekleidung und Ausrüstung der HJ which gives manufacturing instructions for these grey socks.
Verordungsblatt RJF III/10 dated 14.3.1935 mentions the standardised socks (white for Bayrische Ostmark and Hochland at that time and grey for all others). This information was later expanded and it was stated that "white and grey socks are available from qualifying retail outlets and the RZM"
Yes, socks were also regulated. Depending on the type, they had beautiful names such as Jugend, Edelweiß, Alpenstern or Gratspitze. Depending on size and quality, 4 or 5 pfennigs were due to the RZM. Those of the BDM were called Gudrun, Erika, Else or Brunhilde in fashionable brown (modebraun).
The most expensive were the Trachtenstrümpfe/traditional stockings for Bayerische Ostmark and Hochland. RZM tax: 12 pfennigs for the best quality. (RZM Version 1936, p. 127f.)