I am not sure we can lump issues with the gender-neutral man/men and the gender-neutral he together. The first is much trickier than the second, or so it seems to me, though I'm not sure why.
For example, there I am in church on Sunday, and the New Testament reading was about the feeding of the 5,000 (Matthew 14: 15-21), a story that is very familiar to many people including me. But there was an unfamiliar part - I can't imagine why I never noticed it all these years, but it's the very last line: "And those who ate were about five thousand men, besides women and children."
So...it wasn't the literal, mythical or allegorical (depending on how you feel about scripture) feeding of the 5,000. It was the literal, mythical or allegorical feeding of who knows how many but probably quite a few more than 5,000, considering family sizes in those days. And during all these years of Bible study and sermon listening, I thought it was only 5,000. Why? Well for one thing, the person or people who write the subheads you see in some versions of the Bible always refer to it as "The feeding of the 5,000." That was what the subhead said on Sunday, too, and this despite the fact that this was a New Revised Standard version of the Bible, and the compilers of the NRSV have gone to quite a bit of trouble to use gender-neutral language when they can.
And the other reason is that the various people (right up until the person who preached this Sunday) who preached or taught a Sunday school lesson on this passage also called it "the feeding of the 5,000."
So...apparently a whole lot of people, including me, assumed a gender neutrality that was not actually there.
And that's the problem with the gender-neutral man, really. You can't always tell when it's supposed to be gender neutral and when it's not. In, "And those who ate were about 5,000 men," it is not. In "To boldly go where no man has gone before," it is. In "All men are created equal," we now assume it means "all people," but as for what it meant in 1776, I am just not sure. Sometimes, though certainly not always, the only way to tell whether it's gender-neutral or not is to know the mind of the writer. And how often can we do that?
I have never had as severe a problem with the gender-neutral he - some problems, yes, but not nearly as many. As I mentioned earlier in the thread, I do use it, though I also generally take the time to consider if there might be a better alternative. But it's all on a case-by-case basis, at least for me. A careful writer, which is what I strive to be, has to read his (there it is!) work with an ear for how it will read to people who don't know him and never will know him except through the words he uses and how he uses them.