Yes, military and fraternities/sororities attract sexist because these institutions are fundamentally discriminatory based on sex.
Sororities are also discriminatory based on sex, yet they don't appear to have any increased rate of rape over other groups (as far as I'm aware--correct me if I'm wrong). Same with a group of mothers in my hometown who meet regularly to discuss parenting. Did you ever consider that the reason the rape rate is high in the military is because the military attracts people who like violence, danger, and masculinity, and those types of people, who are attracted to these primal instincts, are also less likely to resist other primal urges? All-male prisons (which also consist largely of people who like violence and danger) also have high rates of rape, and they aren't raping women in there.
In countries that are more equal on gender, rates of rape and sexual harassment is also very low such as the Scandinavian countries. In countries where gender equality is non-existent, rape and harassment is very high such as in middle eastern countries.
That's more an issue of governmental sexism than individual sexism. Your argument was that sexist people commit rape, but your evidence points more towards sexist societies have higher rates of rape. While you could make an argument that the reason sexist societies have higher rates of rape is because sexist societies have more sexists, and sexists are more likely to commit rape, that point does not clearly follow from what you argued. Sexist societies indeed tolerate the rape of women much more than societies with legal equality and closer to societal equality. Because it is tolerated as a society, "normal" people commit rape. People do it because they do not value the woman as a normal human being. Compare to slave-owners who considered their slaves sub-human and so justified cruel treatment. Many slave-owners were otherwise completely normal people.
However, in a society where rape is not tolerated, those who do commit rape are going against societal standards for behavior and morality. Perhaps some of them do view women as less than men, but there are plenty of rapists who do not commit it because they don't think women are worth as much as men, but rather, simply because they do not think
anyone is worth as much as themselves and their sexual urges. Likewise, there are plenty of anti-female sexists who would never consider raping a woman.
As for date-rape, you could argue that it is committed by sexist men who do not value a woman's right to say no, but would never dream of "actually" raping her. (Many justify it to themselves by saying, "Well...she didn't
really say no or struggle" even though it was clear she did not want it.) This'd be a great argument, if it weren't for statistics. Looking at
this report, on pages 18-19, you'll see that 1.27 million women 1.27 million men are estimated to have been raped within the year leading up to the survey, though the male rape is not identified as such. It is listed for men as "Made to penetrate". Presumably, since most men could physically overpower most women, the majority of these men were date-raped. So, we're left with two possible conclusions. One, that these male and female rapists are both sexist against the opposite sex, in which case our problem is not sexism against women, but rather that a large portion of men and women hate each other; or two, much more likely, that these rapes are not motivated by sexism, but rather just people who do not value other people's bodies as much as they value their own desires.
Topic: I hate everyone.