There is no question that "they" is becoming the pronoun of choice to refer back to either a singular or plural antecedent. Like it or not, I've seen the statistics and it is where the language is going.
For many people, "he" and "man" is still generic, referring back to men and women. But for an increasing majority of English speakers around the world, "he" and "man" can only refer back to males. Like it or not, this is the way the language is going.
I hear "they" used this way all the time in spoken English. I fact, I have heard it so many times that I doesn't register quite like it used to. But here are the problems.
(1) Written language always lags behind spoken language. While we scarecly notice "they" when the pastor is referring to a single person in the church, we do notice it when the pastor writes "they." Understandable but a little difficult.
(2) Once you have committed yourself to "they," you have also committed yourself to "them," and "them" is still heard, I suspect, marked as a plural even in spoken English.
(3) And "themselves" is only heard plural. The singular/indefinite "themself" is not yet a word in English, although I suspect we are not far from it becoming common place.
So how does this affect Bible translation? Hugely. Take for example Ps 1:1 and v 3. The NRSV goes plural: "Happy are those who do not follow the advice of the wicked .... They are like trees ...." The NLT also uses a plural construction, thus missing the individual thrust of the verse. "Oh, the joys of those who do not follow the advice of the wicked .... They are like trees ...."
The NIV stays singular but starts a new sentence: "Blessed is the one who does not walk in step with the wicked.... That person is like a tree ...."
As expected, the ESV uses "man" / "he": "Blessed is the man who walks not in the counsel of the wicked .... He is like a tree ...." with a footnote explaining the male-oriented language.
All these translations are merely the result of differing translation philosophies, and all acceptable ways to handle the language.
But because English is in transition, we come across difficulties.
Case in point is Luke 9:26. The NIV reads, "Whoever is ashamed of me and my words, the Son of Man will be ashamed of them when he comes in his glory and in the glory of the Father and of the holy angels." When I first read this I thought, "Who is the 'them'?" This is an intensely personal verse. Every single one of us, if we have denied Christ, will stand before the Danielic Son of Man in judgement, and each one of us will give an account for our individual behaior. It is supposed to frighten each one of us. We wouldn't be lost in the crowd.
Another example is Luke 8:8. "“Whoever has ears to hear, let them hear.” I suspect, especially to the non-biblical reader, that the "them" can only refer back to one thing: "ears." Jesus is saying that the ears should hear. Of course, we know that "them" refers to "whoever." But this does not feel like natural English. The NRSV is quite clever at this point: "“Let anyone with ears to hear listen!”
Once English has fully transitioned in this point, many of these difficult passages will simply go away. Until then, there is tension among the translations on this point.
On a person note, I am headed to ETS/SBL today in San Diego. I am going to try and tweet regularly so you can see what is going on. Not sure what the proper hastag is, but you can follow me at @billmounce if you want.