But as the old saying goes: The road to hell is paved with good intentions. 

Languages exist for only one reason: to allow people to communicate with one another. There is no other reason. 

And if we're going to use language to do that, then we must use it with as much precision as we can. If we don't, we defeat its purpose. 

Now there's no conflict between making a language gender-neutral and using it with precision. That is, if you care enough. 

But apparently there are many people who don't. 

And so you get sentences like “Anyone who washes their clothing shouldn't do it in hot water.” Certainly gender-neutral. But just as certainly obscure in meaning. Whose clothing are we talking about? 

Or “When meeting a stranger, smile at them.” Again gender-neutral. And again obscure in meaning. Smile at whom? 

Wouldn't it be better to say instead: Anyone who washes his or her clothing shouldn't do it in hot water. Or: When meeting a stranger, smile at him or her. Two extra words in each sentence. But substantially greater clarity. 

As George Orwell put it: The great enemy of clear language is insincerity. So when you say “their” instead of “his or hers” or “them” instead of “him or her,” you're being sincere about gender-neutrality but insincere about conveying your message clearly. Why not make a conscious effort to be sincere about both? It's not difficult. And you'll be a much better communicator for it. 

Think about it.