I have conflicting thoughts about this.
More often than not this explanation is just used as a excuse to hate whatever group you want while labeling yourself as the good one. But applied to the ultimate consequences most people would still be intolerant.
The classical example of not tolerating nazis because they are intolerant to others, is used because it's a flawless example. The definition of a nazi is a person who wants to eliminate other groups from society just because what they are. A tolerant society cannot exist with them, so they have to go. Perfect.
But we have real life problems when we move from the perfect example to practical cases.
1The "everyone I don't like is a nazi" problem. Someone who wants to be a good intolerant just have to label their opponents as nazis, no matter if they are or not. Just the label is good enough.
While Nazis are used as a classical example. The more pure definition is, that tolerant society should not tolerate people who are intolerant. Thus, only allowed intolerance is the intolerance to the intolerant, any other type of intolerance should then make you a valid target for intolerance.
And here is when I see the biggest problem. That society doesn't usually fit most people values. I would give you several examples. Take billionaires, take robbers, take whatever kind of person you don't like, not only don't like but you don't want anyone like that in your society, for reasons different to them being intolerant. There are other undesirable values in a person that sometimes are worse than intolerance. The lack of tolerance to those people really puts you in the same spot as the Nazi in the paradox of intolerance. As you are hating on people for reasons different than they not being tolerant.
I see two honest solutions and one dishonest one.
The first honest solution is to strictly adhere to the idea of being tolerant everyone but the intolerant idea. Which will imply a higher effort to accept people in the society that you currently don't want to accept. Embrace that tolerance is the ultimate goal and just reject the intolerant, accepting everyone else, no matter what.
The second honest solution is to reject complete unconditional tolerance to everyone but the intolerant. Create a more strict set of values of what the society should tolerate. And embrace the idea that complete unconditional tolerance is a not the goal.
The dishonest solution is just lie about it. Seek excuses, loopholes or overcomplicated cherry picking reasonings on why the people you don't want to tolerate are actually intolerants and then covered by the paradox of intolerance and be happy with it.
To each their own. In the later years I'm feeling myself leaning more for the second honest solution. Unconditional tolerance is not a goal per se. I try to create a developed moral system that could actually be universal and that everyone and anyone could and should follow. And think that maybe I should not tolerate anyone that breaks this ethical rules. Basically instead of saying that the "golden rule" is to be tolerant and that's the only rule that people is not allowed to break. My golden rule is more on the lines of "be a good person", which is harder to define but I think it's more solid, and that's the only rule that should not be broken.
And here ends my TED talk.