Anybody can be prejudiced towards anybody. In my anecdotal experiences of life, women are more commonly sexist towards women than they are towards men.
The “men vs women” war happens and it is real and causes real harm in the world, but it is exacerbated online amid posts/threads that attract gratuitous amounts of attention and create an illusion of it being more widespread than it is. In the real world, in real schools, in real workplaces, people of opposite sexes generally agree and more frequently argue, fight, and judge members of the same sex. The same can be said of other groups, such as the fact that racism towards blacks is rampant and unchecked among the black community. It is a form of self-degradation that is causing severe harm, especially towards African American children and more vulnerable members. We do not yet live in a sophisticated enough century where prejudice towards ones own group is a major topic among the masses. By the 22nd or 23rd century, it’s possible this will be spoken of more. There is a certain social + psychological hierarchy that needs to be climbed, and it is difficult to talk about self-degradation while one is still contending with grievous events such as in Virginia recently.
If we follow closely Jesus’ commands and the writings of the saints, we can avoid participating in the terrible harm that judgment causes and become a font for Jesus to act in our world around us. Jesus loves us so much that he would have died if we were the only person in the world. We must remember that every time we are tempted by the enemy to judge our neighbor.