For those unfamiliar with the idea, "Chekhov's Gun" is the term given to the idea that everything in a story should be there for a reason.
"Remove everything that has no relevance to the story. If you say in the first chapter that there is a rifle hanging on the wall, in the second or third chapter it absolutely must go off. If it's not going to be fired, it shouldn't be hanging there."
- Anton Chekhov
Despite the Star Trek memes that write themselves, it's not a euphemism.
Generally that's pretty good advice. Economy in word choice is a big deal, and trimming down a story in many cases can turn an average story into a good one.
The problem arises when this concept is applied to character traits instead of just characters, scenes, or settings. As a benign example, think about the characters in the novels that you've read: When is the last time you read about a character (even a minor one) who was a cop, a firefighter or a prison guard, and that profession wasn't important to the story? It almost never happens, and that's also why women in romantic comedies have jobs in nondescript offices and the next door neighbor is always a teacher or an accountant. We don't expect anything from these "bland" careers. But as soon as the next door neighbor is a retired FBI agent, well, it's time to expect a shootout.
That sucks, from a story writing perspective. It makes a lot of stories lack flavor and personality when they could have more. But that's not the worst of it. It also whitewashes minority groups out of fiction.
There are some stories where the race of the characters is inseparable from the story, like To Kill A Mockingbird or Crash. There are stories where sexual orientation is inseparable from the story, like The Perks of Being a Wallflower or American Beauty. They're good stories. We need tales where sexual orientation and race are central to the story. But it shouldn't be the only option for non-white, non-straight characters.
In real life, gay, lesbian, and transgender people are all around us. They're not trying to push a "gay agenda" on anyone. They're not "flaunting their sex life," at least not any more than straight people do. For the most part, they just want to do their shopping, go home, change into sweat pants, eat some ice cream, and watch some TV before bed. If not that, then some other variation of the plain old boring stuff straight people do all day.
Pictured: The Gay Agenda
That's hardly ever depicted in novels. Once a character is established as a recurring character with their own name and subplot, if that character is gay, you can bet significant money that their subplot is going to revolve around being gay. After all, Chekhov teaches us, if it's not crucial to the story, why is it there?
It used to be that way with gender. If the main character was male, you could bet that any female characters introduced would be romantic interests. That's changing (slowly), and that's a good thing.
It used to be that way with race. There would be a cast of all white characters or, if the author or director was feeling spicy, they'd toss in a token minority for flavor. That's changing, although it's still an issue.
I hope it changes with sexual orientation, too. It really hasn't yet. There are a few authors out there that are adding diversity "just because" to their work, and their stories are better for it. Too many fall into the trap of starting with a cardboard cutout of a straight, white, relatively young, able bodied male (or female if your book is specifically for women). Then they clone that cardboard cutout for every other character in the story, and if there's any variation in a character, it's a plot point.
Our fiction is still in a place where if a character is white, young, heterosexual, and able bodied, they are able to do anything. Their story could go anywhere. But as soon as a character is different from that "standard," the story is only about that difference.
If you absolutely must make all your characters carbon copies of something, I suggest Captain Jack Harkness.
It's a shame. We, as a people, have the power to write better stories than that. Maybe it's time to (at least when it comes to character traits) put down Chekhov's Gun, and opt to tell richer, more vibrant stories instead.