There’s a substantial tradition of fasting in Christian (especially Orthodox) and Islamic faiths. I’d say that even if we don’t know the mechanism of action, the fact that it was something preserved through the years rather than abandoned means it merits thought about its benefit.
Religious fasting won't induce autophagy. At least in those religious fasting traditions that I know of (Christian lent and Islamic Ramadan) observers can consume calories each day. Autophagy (IIRC) only starts after several days with zero caloric intake.