Yes, the singular “they” “their” or “them” is proper grammar

Over the past few months, many readers have asked if the use of “they,” “their” or “them” as gender-neutral pronouns (such as in the constructions “if anyone thinks THEY can mess with me THEY should get ready for me,” “everybody should mind THEIR business,” “if anyone says it is THEIRS, just give it to THEM”) […]

Over the past few months, many readers have asked if the use of “they,” “their” or “them” as gender-neutral pronouns (such as in the constructions “if anyone thinks THEY can mess with me THEY should get ready for me,” “everybody should mind THEIR business,” “if anyone says it is THEIRS, just give it to THEM”) is grammatically acceptable. Yes, it is. Many style guides are increasingly accepting it, and most everyday native English speakers already use it.
The article you will read below is from the Washington Post of January 8, 2016. Originally titled “Sorry, grammar nerds. The singular ‘they’ has been declared Word of the Year,” and written by Jeff Guo, it points out that linguists of the prestigious American Dialect Society have given their scholarly imprimatur to the singular “they.” So it’s safe to use “they” when you are referring back to indefinite pronouns like “everybody,” “everyone,” “somebody,” “anyone,” “anybody” “someone,” “nobody,” and “no one.”
The traditional grammar rule that “he” should be used to refer back to indefinite pronouns is never obeyed anywhere in countries where English is spoken as a native language. You now risk being called sexist if you use the male pronoun “he” to refer back to indefinite pronouns. For many millennials, the singular they is a non-brainer. None of my students thinks twice about using the singular they; it is older people who occasionally struggle with it.
Although the “singular they” had been confined to informal contexts (and it still is to a large extent, especially among older folks), it is now gaining wider acceptance in formal and serious contexts.
It’s worth nothing, however, that the “singular they” isn’t, as most people think, some newfangled invention in English. As the Economist of February 19, 2014 pointed out in its language column, iconic English writers like Caxton, Chaucer, Shakespeare, Austen, Thackeray, Spenser and others liberally used the “singular they” in their writing.
“It is only in more recent centuries that some grammarians began to insist that the pronoun be singular, and that he should be thought of as gender-neutral. But recent psychological research has shown that the so-called “generic he” does call up the image of a man or boy. In the modern world, it makes little sense to expose young women and girls to repeated instances of A lawyer should know his client’s needs or A good doctor always listens to his patients. And that is even before we get to intersex, transsexual and other cases,” the paper wrote.

Enjoy the Washington Post article below:
Singular “they,” the gender-neutral pronoun, has been named the Word of the Year by a crowd of over 200 linguists at the American Dialect Society’s annual meeting in Washington, D.C. on Friday evening.
In a landslide vote, the language experts chose singular they over “thanks, Obama,” ammosexual, “on fleek,” and other contenders for this annual award given to the most significant term or word in the past year.
Singular they, which The Post officially adopted in its Style guide in 2015, is already a common habit in American speech. An example: “Everyone wants their cat to succeed.”
Earlier, the so-called proper way to say it would have been, “Everyone wants his or her cat to succeed.”
But what gave this word new prominence was its usefulness as a way to refer to people who don’t want to be called “he” or “she.”
“We know about singular they already – we use it everyday without thinking about it, so this is bringing it to the fore in a more conscious way, and also playing into emerging ideas about gender identity,” said linguist Ben Zimmer, language columnist for the Wall Street Journal, who presided over the voting this Friday afternoon.
Old-fashioned grammarians will be disappointed. But others will be shouting: YAAASSSSS! (intj. “expression of excitement, approval or strong agreement”)
Earlier Friday, Zimmer said a win for singular they would also symbolize how mainstream culture has come to recognize and accept transgender and gender fluid people, some of whom reject traditional pronouns.
“It encapsulates different trends that are going on in the language,” he says. “It’s a way of identifying something that’s going on in the language which ties to issues of gender identity and speaks to other ways that people are using language to express themselves and present their identity.
The Post’s style guide ratified this usage last month, which caused some grammar pedants to shriek. But as Post copy editor Bill Walsh explained, the singular they is “the only sensible solution to English’s lack of a gender-neutral third-person singular personal pronoun.”
Zimmer nominated CRISPR (n. “gene-editing technology allowing biologists to alter and control DNA sequences”), a scientific breakthrough that promises amazing – or terrifying – consequences for society.
Past winners have often carried special political or social significance. Last year, for instance, the linguists chose #blacklivesmatter, and in 2011, it was “occupy,” in reference to the Wall Street protests.
On Friday morning, the American Dialect Society had released its candidates for Word of the Year, recognizing the most significant developments in the way we spoke, texted and tweeted in 2015.
Later that day, a crowd of on fleek (adj. “excellent, impeccable”) linguists voted to determine which of the 35 words, phrases, hashtags – or even emoji – deserved the definitive honor, which the ADS has bestowed annually since 1990.
“We’re ultimately looking for words that say something about the way we’re living now, about the way we use words to express our shared experiences,” said Zimmer.
Notably this year, schlong (v. “to defeat soundly”), was in the running, made famous after escaping the lips of Donald Trump. It was nominated for the Most Outrageous category, along with fish gape (n.  “posed expression with cheeks sucked in and lips slightly apart”) and sharewashing (n. “deceptive marketing by companies treating services as ‘sharing’”).
Another contender in that category was a derogatory term for men that is not family friendly. That word launched a thousand thinkpieces when it was featured in a Vanity Fair article about Tinder bros.
Some of the words, like dadbod (n. “flabby physique of a typical dad”) or shade (n. “insult, criticism or disrespect, shown in a subtle or clever manner”) have been so red-hot in mainstream culture that they may have already overstayed their welcome.
Youth slang is well-represented on these sorts of lists, but the terms rarely have staying power. “As the usage becomes broader, they lose their cachet – they lose their coolness,” Zimmer says.  That’s how the ecosystem of American language works.
“Like ‘on fleek,’ has that already peaked? When we met a year ago, ‘on fleek’ was still a little too new, but it really caught on in the first half of 2015. And now it’s the type of thing that a lot of people are sick and tired of hearing,” he says.
The process can be controversial af (“intensifier after an adjective”). Live tweeting from the nomination room Thursday evening, linguist Gretchen McCulloch reported that there was some argument over the spelling of a popular, fabulous way to express joy.
Several of the nominees arose out of the digital dating scene. These days, relationships often begin with an invitation to Netflix and chill (“sexual come-on masked as a suggestion to watch Netflix and relax”) and they end when a person ghosts (v. “abruptly end a relationship by cutting off communication”). And sometimes, the flame is rekindled when someone sends over the eggplant emoji (“male genitalia, sexual innuendo”).
This is the first year that the Dialect Society has allowed emoji to compete for the WOTY title. In addition to the hundred emoji  (“keep it 100,” “keep it real”), linguists also recognized the information desk person emoji (“sassy, sarcastic”), which apparently everyone has been using wrong. But emoji are what you make of them, Zimmer says, which is the beauty of online communication. People are free to appropriate and remix these icons with ZFG (“indication of supreme indifference”).