I don't think 'suppress' works very well because it sounds more like an individual than a society, and because it's more about specific actions than the general attitude.
Ferenczi's original suggestion looks as reasonable as anything for a fairly literal translation. However, I agree that 'instincts' is broader, vaguer than 'drives.' Maybe 'instinctual drives' would help get the idea of desire in there a little better.
But I guess my beef is with the German word in that context in the first place. I don't think the Islamic Republic is necessarily against instincts -- think of, say, an instinct for self-preservation, an instinctive avoidance of danger. Someone could even make an argument that Islamic law isn't even necessarily against sexual drives, only against the public expression of sexuality -- and not just homosexuality BTW, though it does tend to be repressed more strongly, but also heterosexuality. Or sensuality, maybe, if you include the music -- that's not necessarily an expression of a sexual urge, or is it?
So Triebfeindlichkeit does seem to be being used as a euphemism or shorthand for a whole constellation of things. Puritanical is another word that tends to be rather casually thrown around like that, meaning, loosely, anti-sexual or anti-sensual, so puritanism might be as good as anything.