Many countries, neither "backward theocracy" nor "horrendous dictatorship", have prohibitions on induced abortion, excepting cases where it is to save the woman's life. The Philippines, Bangladesh, Malaysia, Indonesia would be some examples.
However, in most of these places, there's a subterfuge -- "menstrual regulation" or "d&c" -- and also quite a bit of wink-wink, i.e. the authorities know it goes on in clinics, but as long as no more makes a campaign issue of it, everyone conspires to pretend it doesn't happen. Hardly satisfactory, as access to these clinics depends upon word of mouth which means many continue to seek out backstreet abortions, complications being treated in the hospitals.
There are also -- sometimes dangerous -- 'traditional' herbal potions for inducing abortions; but these are rapidly passing out of the knowledge base as modern medicine takes over.
kj khoo