The Milgram Experiment does give an explanation for the blind obedience of citizens during mass genocides and murders, such as the Holocaust. There were many factors that affected obedience levels in test subjects, such as reactions by the learners, proximity to the learner, and the proximity to the experimenter themselves. If the learner had a louder, robust reaction, the teacher was less likely to obey, but if the learner had a more contained reaction, the teachers felt less guilt for their actions. If the learner was placed far away from the teacher, the teacher followed commands more easily, but if the learner was closer, or if the teacher was forced to make physical contact to punish the learner, the teacher was far less likely to follow what the authority figure was telling them, only 30% obeyed under these circumstances. But, if the experimenter, or the authority figure, was close to the teacher, the teacher felt more pressure to obey them, and follow their orders, no matter how badly they were hurting the learner. This evidence shows that if ordinary people do not have personal connection or physical proximity to another group of people who are being persecuted, they are more likely to blindly follow the lead of an authority figure, even if that authority figure is inflicting immense pain on innocent people.
But, what this experiment doesn't explain, is the thoughts of the people who are leading the ordinary citizens. These people drew up and executed plans of mass murder against another group of people, and have risen high enough in the social order to have power over masses of people, enough to create an army that is capable of committing such atrocities. These are the people who, given the role of the teacher in the Milgram Experiment, would've been fine inflicting pain on another person, no matter the proximity of the learner or the experimenter. They do not follow social order and standards. They are "free thinkers" and nonconformists, but not in a positive way.
In Rethinking One of Psychology's Most Famous Experiments by Carri Romm (2015) , it says "Though the term didn’t exist at the time, Milgram was a proponent of what today’s social psychologists call situationism: the idea that people’s behavior is determined largely by what’s happening around them." For example, in the Holocaust, the ordinary citizens, who had no connection to the Jewish culture, blindly joined the Nazi Army, because that is what they were being told to do by an authority figure, but also because that is what everyone else around them was doing, the same way that the proximity of the experimenter and the lack of personal relation to the learner made the teacher more susceptible to influence and more likely to obey the authority figure.
In response to this experiment, I think society would benefit from the encouragement to not exactly disobey authority figures, as regulations are needed to keep peace and contentment, but to foster empathetic and sympathetic mindsets. The ability to understand the thoughts and feelings of another is what will keep violence, genocides and murders at bay. Acceptance of differences and being able to not conform to the majority would create a peaceful and safe world.