Here is the etymological information M-W provided:
"Palatable" comes from "palate," a Latin-derived word for the roof of the mouth. The palate was once thought of as the seat of the sense of taste, so the word eventually came to mean "sense of taste," or broadly, "liking." "Palatable" has been used in English to refer to palate-pleasing foods since 1664, but it isn't our only — or our oldest — adjective for agreeable tastes. "Savory" dates from the 13th century. "Toothsome" has been around since 1551. "Tasty" was first used back in 1603. And "appetizing" has been gracing culinary reviews since 1653.
Since there are two meanings this brought to mind two things:
For the time will come when they will not endure sound doctrine; but wanting to have their ears tickled, they will accumulate for themselves teachers in accordance to their own desires, and will turn away their ears from the truth and will turn aside to myths. - Timothy 4:3-4
The "they" Paul refers to in this passage are seeking doctrine that is "palatable"... pleasing to them.
Such a doctrine might include the idea that G-d's instruction regarding what food is suitable somehow no longer applies. This false doctrine might teach that we can eat anything we find palatable... perhaps.