I would never consider a goblin as fey.
I am guessing you have never read a reallife fairytale about a goblin?
Essentially, gnomes and goblins are ‘sprites’ (childsize nature spirits who personify the land that humans inhabit).
The gnomes are helpful fey spirits (as long as the land is treated respectfully). Oppositely, the goblins are harmful fey spirits.
The ‘gnome’ is a less accurate word that is used to describe similar sprites going by various regional names, such as: fairy (as Shakespeare describes them), hob, brownie, leprechaun, and so on.
Tolkien ‘hobbit’ is a variant of ‘hob’.
A ‘hobgoblin’, is a contradiction in terms being both ‘helpful’ and ‘harmful’ at the same time, and is the nickname for a childlike sprite that plays humorous painful pranks, but in a good-hearted way. Inspiring laughter is helpful. For this reason, I like to play D&D hobgoblins as Good or Neutral practical jokers. Sometimes the crazy stunts on internet can serve as inspiration. Heh, the more intelligent hobgoblins can be a real menace.
Originally, sprites were understood as appearing as if human children. But over time, the sprites came to be understood as shrunken spirits, appearing as grown adults who were the size of children.
Anyway, goblins are about as fey as a concept can get.
I like how the 4e makes halfling originate in the material plane, and the gnome originate in the fey plane. If I remember correctly, the 4e goblin is fey as well.