He definitely is saying that there are clear issues that all moral beings should be able to agree upon. Honor killings of family members who did nothing wrong? We can agree that's wrong...only, we can't all agree that its wrong, because people still do it and they think they are right. His point is that even if we can't all agree, we still don't have to respect their opinions, because a substantial majority can recognize that they are wrong and the minority view should be suppressed. I think that is clear for some things, such as consequential acts (acts which have physical effects on people...like honor killings). It is less clear on non-consequential acts (having kids spend 8 hours a day memorizing the Koran). He might argue that having them do that stunts their well-being curve...and he may be right. But freedom is what prevents us from imposing our view on others. He is arguing that freedom should not trump all things, and prevent us from stopping evil. I agree. The issue is where do you draw the line. Does he draw the line in a different place than I do? Does Obama draw the line in another place, and Trump in another, and Hitler in another? Obviously. Do we just defer to majority rule? That can be very oppressive...in fact, majority rule leads to some of the oppressions he names.
Yes, the extremes can be condemned, and freedom can sometimes be sacrificed in favor of promoting good (imposition of good in violation of people's wishes). Yes, there is a reasonable middle ground, in which freedom should not be sacrificed even for more supposed good. And yes, there are people who will use his "I can judge" paradigm to do good, and there are people who will use that paradigm to do evil in the name of doing good.
If he is arguing that we need not let the gray areas block us from taking action when things are black and white (and I think he is arguing that), then I agree. But, constant vigilance is required, to watch for people who would, for example, infringe on parenting rights just because they claim to know better, when in fact they may not know better, even though they may have the power of the state or a majority of the population behind them.