The first English usage of palatable cited in the Oxford English Dictionary comes from 1619, and it is already being used in a figurative way:
1619 | It [sc. sin] may taste pleasing and palatable at first, but Leuen is not sowrer at last. T. Adams, Happines of Church 377
In other words, taste already had a lively figurative sense to it, and so palatable, pertaining to taste, could be used to describe something not literally tastable at all, sin. The OED gives this figurative sense of the word its own definition, with uses dating from 1683 ("Truth...is seldom palatable to the ears of kings"), but given the first quote above, it's highly likely other figurative uses were cropping up before that, making a variety of non-food things figuratively palatable. For example,
I did not attemper my History to the Palat of the Govern∣ment; so as to sweeten it with any Falshood; but I made it Palatable thus far forth as not to give a wilful disgust to those in present Power, and procure danger to my self, by using any over-salt tart or bitter Expression, better forborn than inserted, without any prejudice to the Truth. (Thomas Fuller, The Appeal of Injured Innocence, 1659, EEBO)