Red chili peppers are different from the Italian horn, but some traditions say the horn symbol was modeled after a red chili pepper which grew in abundance in some areas of Italy.
Generally, they are worn or hung in places to protect people from the evil eye. Plastic renditions of chili peppers are also carried in the pocket as a good luck charm.
In the Chinese practice of Feng Shui, there is a superstition that a business can hang about seven fresh chili peppers inside its door which is said to bring income to the establishment. However, the chili peppers must be replaced or removed before they dry up because leaving dried peppers on the door is said to create bad luck. Practitioners claim this superstitious practice only works for small businesses rather than for larger corporations.
I have also come across some evidence that the stringing of seven green chilies and a lemon is said to bring good luck to a home. This contrivance is to be hung in a safe part of the house, usually under a table, and left there until the following Saturday when it must be burned and substituted with a new one.
"Hindus believe that this device drives bad spirits out of the house," explains this blog.
Christians rely on Jesus Christ for protection from evil spirits and belief in talismans such as this is considered a superstition and an offense against the First Commandment - "You shall have no other Gods before Me" - by the Catholic Church (CCC 2117).
In a nice way, I would definitely mention this to whoever is displaying the peppers because he or she might not be aware that this is a non-Christian belief, or that displaying them in a church could cause someone to think the use of amulets is okay.