Where and when did “whack” become slang meaning crazy or appalling, such as in the phrase, “that’s whack?”
Whacko has been slang for a crazy person since I was a child. I think it coming from “whacking off.”
No cite other than my own recollection, but I remember the phrase “Crack is Whack” popularized by Keith Haring from the late 1980’s.
Wait…
I don’t know the veracity of Urban Dictionary, but see the third definition here.
Wiggity-wack!
Good old Kriss Kross. “Jump” was #1 on Billboard for 8 weeks in 1992. I put my pants on backwards just Tuesday and was thinking of them.
I think it was around before then, but it became fairly prominent/popular slang in the early 90s.
Wacky to mean =Crazy, mad; odd, peculiar(OED) shows up in 1935.
I doubt that whacking off had anything to do with it. You not only didn’t go crazy, you didn’t go blind. 
Wacky?
Wacky to wacked out to wack. Americans love shortening slang!
Urban dictionary lists “wack” (no h) as meaning lame, sucky, or low quality. It doesn’t say so, but I WAG this usage may come from or at least be influenced by the word “weak.”
Bugs Bunny short, 1942: The Wacky Wabbit
But whack and wacky are not the same words.
From what I’ve seen, spelling proficiency is not a high priority among the nation’s youth. The absence or presence of an H seems inconsequential.
Actually it is quite often spelled “wack” – as in the film, set in 1994, The Wackness.
“Americanisms–old & new” 1889 “In Virginia, machinery is said to be out of whack when out of repair”
“The Poultry Chum” 1886 “I have some chickens hat are out of whack, but I don’t know what it is or what will cure them.”
“Slang and its analogues past and present” 1904 “Whacky, subs, (tailors’).— A term applied to anyone doing anything ridiculous or FOOLING ABOUT”
“Glimpses of the cosmos: Volume 4” 1915 “I walked down a London street on the first Sunday morning after my return congratulating myself that I hadn’t come back “wacky” like some of the boys. It was good to be there and alive.”
“Good Housekeeping” 1941. “Other unattractive terms in this avenue are…whacky or wacky: crazy — discordant and noisy”.
Whether the use of “Out of wack” to refer to something crazy or appalling indirectly linked seems unclear, but plausible IMO. Wacky meaning crazy seems to have slipped into English usage by the early 20th century and been well understood by 1915.