Voadam
Legend
Elven Chain Mail
(From DMG...revised 241)
This is magical armor so fine and light that it can be worn under normal clothing without revealing its presence. Its lightness and flexibility allow even BARDS and THIEVES to use it with few restrictions. Elven fighter/mages use it without restriction, however, it is rarely sized to fit anyone other than an elf or a half-elf.
Bolded words were not bolded in text, I put the bolding in there to point it out. Also, note, you had a 20% chance of getting man-sized elven chain if you found it, but Half-Elves could also be Bards.
Yes they can use it. It does not say they can cast in it.
It says they can use it in the PH too. "He can wear any armor up to, and including, chain mail, but he cannot use a shield."
Same for thieves "A thief can wear leather, studded leather, padded leather, or elven chain armor. When wearing any allowed armor other than leather, the thief’s abilities are penalized (see Table 29)."
I would place the bolding in a different part of the sentence.
"Its lightness and flexibility allow even BARDS and THIEVES to use it with few restrictions."
One of those restrictions is penalties to thief skills, another seems to be casting in armor.