Most readers consider the extent to which they can sympathize with a character. When they encounter an unsympathetic character, one who is difficult or impossible for them to relate to, they toss the book aside. “Who cares,” they may say.
In truth, it is more about what the writer shows us than whether we can to relate to superficial aspects of the character. Relateable is perhaps the wrong word; instead, I like the word human. It’s a much better approximation of how I read and “relate” to characters. Is the character a person? Do they have complex problems, a rich and painful past, and a variety of sometimes competing hopes, dreams and fears? Yeah? Then count me in.
This, of course, is the macro approach. The best characters may be complete fools or weirdos, but when they’re written right, with as much kindness and compassion as you can afford them, we pause to appreciate their humanity. Still, there’s a lot of content out there, so I don’t fault people who stop reading a book or story simply because a character does or says something that is a complete turn-off.
George Saunders puts it very well (of course!):
In the early drafts, you may create a caricature or a character that you’re looking down on, getting some jokes out of. But the story’s form doesn’t like that. The story’s form doesn’t like condescension or puppeteering, so it responds by being boring. The reader feels it’s a static story, that the writer is holding all the cards and dominating his characters.
As you try to address that in revision, the characters mysteriously become fuller, because as you reconsider them you’re actually loving them more. You’re paying closer attention to them. You’re listening a little more closely, and so the sum total of the story gets funnier, smarter, faster, and the characters come to be more equal to the author.