Sexism can get perpetuated unknowingly in all sorts of was via the law. I suggest studying the book Legalizing Misandry by Katherine Young and Paul Nathanson to see how this can happen. The law also has all sorts of effects on what happens on college campuses and how sexism either gets continued or abated.
We know that at present there exist programs for woman to get ahead in academia, because of their gender, but extremely few, if any, in comparison for men. Have you ever heard of a scholarship program that specifically targets boys in the humanities where they are a minority now and have historically come as a minority also?
There exist only three non-religious male colleges in the U. S. There exist many more women's colleges.
There exist women's studies programs, but male studies programs have trouble getting a foothold in academia. Ryerson makes for an interesting example. Sexism, in the form of misandry, has popped up before when a men's group formed.
Women make up the majority of graduates in the U. S. in terms of high school degrees, associates degrees, bachelors degrees, masters degrees, and doctoral degrees. Trends also come as revealing.
Also, some campuses have a standard of "preponderance of the evidence" for rape cases, which in effect eliminates due process mostly for men, but not for women, and such a standard thus effectively consists of a sexist policy against men. Some other policies can unintentionally end up sexist against men as a study of Daphne Patai's Heterophobia makes clear.
Male sports teams getting cut also comes as another way in which a policy has ended up sexist unknowingly.
If you want to avoid sexism in academia and elsewhere you need to care about men in general just as much as you care about women in general.
Sexism can perpetrated by people by having policies that require different standards for people of different sexes.
In order for a male to get student loans in the United States he has to register with the selective service system (which is still a real entity). No female has such a requirement placed upon them in order to obtain such a loan.
Sexism can get unknowingly perpetrated by believing that an educational equity for one sex can qualify as sufficient for both sexes. The Women's Educational Equity Act is one example of this.
Lifestyle, knowledge of one's educational opportunities, and health in general can all effect academic achievement as well as one's ability to achieve academically. I can't speak to the extent of things here, but one person had the following to say:
"As I have said here before, I have worked in higher education for thirty-one years and have never seen a poster or service announcement on any campus aimed at promoting positive lifestyles, health, educational opportunities, etc., for boys and young men. I have seen numerous ones for girls and young women."
Sexism can also get perpetrated in academia via "equity hiring" as Janice Fiamengo makes clear...
"Next came the creation of a shortlist of three or four candidates for interview; some members of the department were keen to stack the list with members of the diversity groups. To this end, there was much sophistry about why a (white) male candidate’s book with a prestigious university press was really no better than — was actually perhaps a bit inferior to — a female candidate’s single article with an academic journal of no repute; or about why a (white) male candidate’s expertise in highly competitive Shakespeare studies was no better than — was actually far less original than — a female candidate’s untested, largely speculative work on an obscure seventeenth-century woman playwright. Thus were well-qualified white men kept out of the competition. Moments of levity occasionally occurred when we were forced into elaborate interpretative dances to determine if a male candidate might be black or Asian or gay, though usually the savvy candidate made that clear in his cover letter.
At the hiring stage, there was the same special pleading. Poor presentations by women candidates were praised as “provocatively unorthodox” or “strategically unconventional” while polished ones by men were criticized as “safe” or “unoriginal.” Women’s mistakes could be overlooked or seen as strengths (“I like that she was courageous enough to present on material that she is still working through”) while men’s mistakes were definitive (“I’m shocked that he could be finishing a PhD and still not know that [minor detail”]). One male candidate who had given the best demonstration class I’d ever seen was criticized by our leading feminist professor — presumably because she could find no other faults — for having never visited England to do archival work, a criticism the poverty-conscious lady would almost certainly never have made of a struggling single-mother candidate. That a man might have life circumstances preventing him from travel seemed not to have occurred to her."
That hiring practices may more often than not, favor the hiring of female candidates over male candidates gets further suggested by this experimental research.
The number of answers which only address sexism against women here, without also addressing sexism against men makes it very clear that you can NOT eliminate or reduce sexism by focusing exclusively on the needs or interests of just one sex. In fact, that comes as a way to perpetuate sexism.
This document starting at about 532 suggests things goes even deeper than this answer has merely outlined.
The University of York recently withdrew it's intention to mark International Men's Day.
The key to avoiding sexism lies in fully understanding the plight of all sexes and acting accordingly.
And no discussion of sexism in academia is complete without at least some indication of the issues of trans-people in academia.