Pronouns, like other grammar tools, are very important. We've been using them for so long that they have become a serious part in our conversations about people other than ourselves. I wouldn't necessarily say that they've just suddenly become cool. I would say our interest has recently increased towards the subject when it comes to using the correct pronoun, as it shows our understanding of the identity of the person we are speaking about. Because someone's identity is important, their pronoun should be just as important. I think looking at pronouns as simply just a "part of speech" as Baron says is only looking at the basic layer of what a pronoun means. Messing up someone's pronoun can spark some conflicts, depending on the individual mentioned.
But when you look at "they" (singular) versus they (plural), their doesn't seem to be an event where conflict would arise. I may have used they in reference to a singular being before, but I don't think there has been a time where it's crossed my mind to contemplate if what i'm saying is weird. Then again, I can't really think of many clear examples where I've used they as singular. I typically use he or she, since I tend to know the correct pronoun for the identity of the person i'm referring too. I guess myself, like others, may not see the distinction between the two as such an important topic, so we overlook it. But, since we've discussed how important semicolons and oxford commas are, maybe I'll start paying attention a little more.