Something that is almost unimaginably unacceptable is unconscionable. Think of it as being something that no reasonable person would even think of doing or saying — something unbelievable, outrageous, and often horrible.
The word unconscionable is related to the word conscience. Add the un-, and you can see that it refers to something done without applying good moral judgment. The word first appeared in the mid-16th century — presumably everyone up until that time had high scruples and never did or said anything beyond the boundaries of conscience. Sadly, the antonym, conscionable, is rarely used, and, in fact, has been obsolete since the 18th century, though unconscionable remains in frequent use.