On the whole gender-neutral third-person-singular pronoun thing: "they" and "their" when used such as in "looks like somebody lost their wallet, they can re-claim it at lost and found," are grammatically incorrect, although unfortunately quite widespread. Is the widespread nature of this grammatical foax pas due to a failure of Our Educational System to impart or even value correct language use, an artifact of our egalitarian values and/or the rise of feminism, or just because humans are grammatically lazy?
Variety in language is driven by humans leaving off sounds and words here and there, omissions are transmitted through the generations until the omission becomes the norm, and room for another lazy change can begin and eventually multiple mutually incomprehensible languages result. Now that we have written language this phenomenon has been greatly retarded, so that our English resembles, more or less, the English of three hundred years ago mines thee speelling--but lazy options still exist to be exploited and eventually made into mainstream. Language will still change, eventually. Thus, although sloppy, although irritating to Those of Us Who Care, "they" and "their" as singular pronouns are certainly here to stay. If you use 'em, you won't be alone.
Although on the subject of gender-neutral pronouns, and the use of the "new" correct grammatical form: "looks like somebody lost his or her wallet, he or she can re-claim it...", as opposed to the "old" correct grammatical form: "somebody lost his wallet, he can re-claim it..." (no matter if the wallet-loser was a he or a she, when we don't know), I have this series of things to say:
Yes, you could disparage gender-neutrality in speech or written text as mushy over-the-top-political-correctness, pronouns being just words. You could assert that we're all Adults (of Both Genders) in this world, we can use our considerable powers of intellect and observation to realize that the general "he", "Man" and "mankind" actually imply both genders--so stop getting your panties into a twist over it. ("Get your panties in a twist"--gender irony in that statement, much, that I just used with wild abandon?)
Personally I take a middle-of-the-road view of the subject (and I do try to use "he or she", or else rephrase third-person-generalities to be plural, or dispense with pronouns and just refer to the subject directly). It is true that my life is not destroyed or invalidated by reading "he", "his", "mankind" all day long. I am quite able to extend a mere sonoral and symbolic representation of an idea to encompass both sub-categories of human and can remind others that they ought to be doing so as well. Furthermore, I do not need the approval of the authors nor explicit symbolic acknowledgement by them* in order to be a living, thinking, reading, participating member of the human race or otherwise affected by whatever subject matter this symbolic-of-both-genders "he" is involved in--not that most of these authors are consciously trying to deny my status thereof by failing to write "he or she" for whatever reason they fail to do so.
So I agree that it does not matter what pronoun one uses, not substantially. Especially not with all the other gender issues in our culture that are extremely whacked: the frigid/slut dichotomy (and the particularly chauvinistic notion that those who fall into the "slut" category deserve no respect and have no boundaries at all including personal safety), men who act like Mel Gibson, that whole unattainable beauty norm thing, and not when we have for across-the-ocean neighbors people who drop acid on schoolgirls. To name a just few, and only things related to being female. In that sense, who cares about some pronouns in the English language?
It doesn't matter, in comparison to a lot of other things that DO matter, but it does make a difference. Words and word choice are not and will never be meaningless. Human interaction is about meaning, and words--especially in non-face-to-face interactions like news, books, articles, the 'net--are how meaning is relayed from one person to another. The collective experience of someone who encounters pronouns that are sometimes used to differentiate one sub-category of human from her category and must recognize the instances in which that pronoun should be taken to instead include her sub-category as well is a different experience than that of someone who reads things about humanity and doesn't have to constantly do slight, subtle mental gymnastics to feel included. The difference isn't hard to recognize, but the issue is not about how hard it is to make that mental correction, it is about the subtle but real social implications of not being explicitly included. It is no difficulty, relatively, no terrible hardship--but it is a real difference, and one that doesn't take a whole lot of effort to alleviate.
So when I read, say, a physics book, or any kind of science or philosophical writing that describes "humans" instead of "man", that describes the experience of a physics student and sometimes refers to that student as a "she"...it makes a difference to me. I don't have to remind myself that the author most likely meant me too and if he didn't then screw him I don't need his damn approval to contemplate a physics problem or human development--with some inclusive pronouns every once in a while I don't even have to go there. Then I know I am not an afterthought, not that exception to the rule that says people (and especially physicists) are male unless otherwise differentiated. I'm just someone who is involved.
Inclusion is vitally important to a species as intensely social as Homo sapiens, and when inclusion is explicit rather than merely implied, that is a difference. Furthermore, inclusion in something as weighty as our evolutionary or cultural history (where "man" "man" "man" is prevalent) or our understanding of the physical world is, you know, a Big Deal. Those things affect and are affected by both genders and were so even before we started remembering to include the female when we wrote about them. It is thus not out of political correctness because now we value that sort of thing that we adopt gender neutral speech, rather we are being true to exactly whom has always been involved. Even in physics.
So when an author makes that extra step, when he or she makes sure the hypothetical humans in question are not Default Male or not only Default Male...(by using he or she, since good authors aren't going to make the mistake of using "they", oh no) it makes my day that might lighter, that much better. I think "you know what, thanks."
*Them, they, their/s, are third-person plural pronouns, in this sentence the subject being replaced with a pronoun, "the authors", is plural, and so it is gramatically fine and dandy to use the third-person plural pronouns in this case.