The ways in which the leaders of Gilead (i.e., men) claim to protect women are, in reality, ways in which women are suppressed. By dictating what women wear, banning women's literacy, and so on, these men are eliminating the mechanisms by which women can think for themselves and express individuality. Women will rebel against this act of suppression and assuming what is best for women. That is not to say that women are rebellious in nature. In modern society, and according to the principles of feminism, women should be given the same rights as men and be treated in ways that are equal to the ways men are treated.
Men are not violent by nature. In the case of the Republic of Gilead, in which men are indoctrinated into believing that they are superior in virtually every way (with the exception of childbirth, in which the handmaids of Gilead are treated as holy and valued), they will use that which is given to them by God to assert their power. In the novel, Gilead is structured based on Christian theology, and the idea of male superiority is rationalized by distorting and manipulating God's principles.
To ensure that both women and men can live in circumstances of safety, equality is imperative. In accordance with democratic principles, in our world, both women and men can be charged based on acts of aggression and abuse. These are the ideal circumstances, although the ways in which these laws are enforced are flawed. For example, when reporting an individual for sexual assault, there must be evidence supporting the alleged acts. But there are many cases in which women do not report incidences of sexual assault in the immediate aftermath, whether this is due traumatization, gaslighting, intimidation inflicted by the prosecutor, or other circumstances. As such, it is difficult to obtain evidence after the fact.
Considering potential governmental means to ensure safety for everyone is a very broad topic. Due to issues pertaining to sexism, homophobia, racism, and so on, actual investigation, evidence-gathering, analysis, and persecution are biased. In an ideal world, every single person, regardless of their identities, would be treated equally. Unfortunately, this does not actually translate into people being treated equally in accordance with the law.