There is a spicy vegetable grown in a number of places, most prominently in the state of New Mexico. It is commonly green when it is picked, but may be dried to a bright red. It is called chile. It is served in many restaurants as both red chile and green chile. That's the source of the official question of the State of New Mexico: "Red or Green?" (The appropriate answers are red, green, and Christmas [both].)
Chile is quite a different thing from chili (more properly identified as Texas chili), though some form of chile is used in preparation of that dish.
Most outside the Southwest are pretty ignorant about chile. I was once in a diner in Arlington VA where I saw a menu item that said Chili Omelet. I thought "This is great!" 'Cause I hadn't expected Arlington would know anything about chile. I asked the waitress "What kind of chile is that?" When she got a terribly puzzled look on her face, I tried to help: "Red or Green?" She thought for a second and said of their chili that "It's kinda brown. From a can." I'd been right in the first place: They had no idea about chile. No concept.
The Associated Press is in the same condition. Their style guide apparently specifies that the proper spelling is "chili" with two exceptions when specifically referring to Hatch Chile (chile grown near the town of Hatch in southern New Mexico) or when referring to the South American country of Chile.
A New Mexico newspaper writer objected, and tried to get the Associated Press to correct their style book. But she kept getting rebuffed. Finally she went to New York to speak directly with the executives in charge of the style book. She made her case to them. They responded in a rather patronizing manner. They explained that, if the style book called for spelling chile correctly, people would confuse the vegetable with the South American country.
The New Mexico writer was exasperated by this answer. She responded to them with words like "Well. that hasn't been a problem with Turkey!"
Does this mean the Associated Press thinks its public is stupid? I'd say it does!