It is actually very easy to avoid sexist language; our culture continues to use it out of desire, not convenience. Starting at the top, most churches still call God "He," though they could just as well say "She," or--more appropriately--alternate between the two.
Americans use bad grammar rather than deal fairly with gender. Consider this sentence: Everyone at the protest said ___ was taking time off work to march.
The average American says Everyone at the protest said they were taking time off work to march. That is grammatically incorrect because "one" is singular and "they" is plural. This is a common (and highly irritating) grammatical error made by many people, regardless of reason, but now that people are all confused about gender, it is even more common.
Classical (sexist) language usage would be: Everyone at the protest said he was taking time off work to march. And if the march consists of all men, that is also functionally correct. If the march consists of all women, the sentence should be Everyone at the protest said she was taking time off work to march.
But if the march consists of both men and women, or we don't know the gender of the marchers, the habit among people with good grammar is still to say "he" and the habit among those with poor grammar is still to say "they." However, people (with good grammar) who are sensitive to the existence of two genders will alternate the use of personal pronouns. For example: Everyone at the protest said he was taking time off work to march. Some of the marchers risked losing their jobs, most of them came from a great distance, and everyone agreed that she was making a worthy sacrifice.
Another useful rule is to use yourself as a reference point. If you are female and writing and talking about a group whose gender is mixed or unknown, you may say "she" since you are a woman and it is natural to make the association--men have been doing it for centuries.
Just last night, Jay Leno had Misty May and Kerri Walsh on The Tonight Show (May and Walsh, who travel with a group of scantily clad "cheerleaders" who draw viewers for the two volleyball players, are about as politically unevolved as you can get, but that is another story), and proceeded to refer to them as "guys" throughout the interview. "But that's a traditional part of our language!" you say. Exactly. It is traditionally sexist. What would it have sounded like if Leno had had Justin Gatlin and Shawn Crawford on and called them "gals"?
A few days ago, Anson Dorrance--former U.S. National Soccer Team coach and head women's soccer coach at the University of North Carolina--was on the Today Show talking about the U.S. women's olympic soccer team. It is fair to say that Dorrance has done more for young women than most women have, and it was with great pride that he called Mia Hamm "the face of women's athletics."
Asked about the personalities of both Hamm and Brandi Chastain, Dorrance said of Chastain, "She's a great showman." So ingrained is sexism in the English language that even Dorrance--who knows first-hand what women go through in trying to achieve their goals--called one of his prize players a man. Chastain isn't a man; she is a great showwoman. And the women athletes who play fairly and graciously are not "sportsmen."
So-called "political correctness" is now derided, partly because it has been misused by idiots (consider the "niggardly" case), but mostly because people do not want to change. Look at it this way: It is not politically correct to call a woman a woman; it is just plain correct.