It is said that non-brahmins are not allowed to recite the vedas. However, are they allowed to read any of the spiritual texts or scriptures? What about the upanishads, the puranas, etc.?
Srmadbhagavam says (1/4/25) that "trayi" (which means both the A-U-M and the three vedas, should not be heard by women and the fallen dwijas and sudras.
The Vedas include the Upanishads.
So the traditional belief says only dwijas who are initiated by Gayatri mantra and perform Sandhya-Vandana regularly canread the Veads.
All other scriptures like the Itihasa, the Puranas, the smritis and Tantras can be read by the non-brahmins.
These apply only to those who want to get the results of reading scriptures as described in the scriptures. For intellectual interest, anybody can read anything.
Following 'Adhikara' and 'Anadhikaara' are only for those who have sraddha for iur tradition and culture.