Gremlins struck gold with Jerry Goldsmith. His style is all-over-the-map, which is a great match for the genre-defying Gremlins. Prior to Gremlins, Goldsmith scored Planet of the Apes (1968), neo-noir Chinatown(1974), and horror classic The Omen (1976).
Gremlins can be seen as having elements of all these films. There's a literal Chinatown scene at the beginning. The mogwai are a bad omen for Kingston Falls. And Stripe points guns at people like famous NRA advocate and Planet of the Apes star Charlton Heston.
Goldsmith's Gremlins theme is the perfect complement to the film. It starts sweet and innocent, like a Christmas carol, then transitions into something rambunctious and possibly sinister…which is also like a Christmas carol.
Hey, have you ever actually listened to "Rudolph the Red-Nosed Reindeer"? Santa is a jerk.