Ever since I wrote The Eye in the Stone, I have tried to tackle the problem of “he or she” versus “they.” If the pronoun refers to a single unknown person, e.g. “Someone stood in the doorway, in total silhouette,” I can simply use he, or she, if the gender is apparent to the narrator, even if the person can’t be identified. If the gender is not obvious, I may use “they” instead of “he or she.” This is a rather clumsy example, I know, but it will serve.
I have tried very hard to avoid using “he” as a neuter pronoun. One of the conventions I have used is “they.” Certain purists will object that “he or she … they” does not agree in number. They should also note that “he or she … he” does not agree in gender.
The real problem, of course, is that in English today, we do not have a true neuter pronoun, other than “it,” and I think almost everyone will agree that “he or she … it” is an abomination. After all, we do not mean that he or she is a neuter it, but that the person we refer to is either male or female but not specified. And not neither or both.
There is precedent for the use of “they” as a neuter pronoun, to be found in the Oxford English Dictionary (Oxford University Press, 1971), i.e.: They … signification 2. Often used in reference to a singular noun made universal by every, any, not, etc, or applicable to one of either sex (= ‘he or she’).
Examples of this usage date from 1526 to 1874. “They” has been used as a neuter pronoun by both common speakers and by literary figures. It is the natural thing to do. It may be the best solution we have.
Today, only a pedant will pick on the disagreement in number, though anybody can be pedantic at times (as I have sometimes been on other subjects, not always seriously). In current social consciousness, the problem of sexual equality and gender chauvinism is much more important than mere number. If you can think of a better solution, let me know. A better one, not just a different one.
I would like to refer the reader to Handbook of Non-sexist Writing, by Casey Miller and Kate Swift (Lippincott & Crowell, 1980). It is a calm, well thought out, sympathetic discussion of the problem, which every reader, writer, speaker, and publisher should read.