The paradox of tolerance, as it is commonly argued, has to be one of the worst philosophical arguments actually taken seriously. It basically boils down to an argument from fear - We all believe in the importance of {Sacred Value}, but the Evil Ones are coming to take {Sacred Value} away! By using our own good natures and {Sacred Value} against us, they will claim power, and then destroy {Sacred Value}! The only way to stop them is to destroy {Sacred Value}, thereby depriving them of the ability to use it against us!

Incidentally, here's what Karl Popper himself had to say on the matter; "Less well known [than other paradoxes] is the paradox of tolerance: Unlimited tolerance must lead to the disappearance of tolerance. If we extend unlimited tolerance even to those who are intolerant, if we are not prepared to defend a tolerant society against the onslaught of the intolerant, then the tolerant will be destroyed, and tolerance with them.—In this formulation, I do not imply, for instance, that we should always suppress the utterance of intolerant philosophies; as long as we can counter them by rational argument and keep them in check by public opinion, suppression would certainly be most unwise. But we should claim the right to suppress them if necessary even by force; for it may easily turn out that they are not prepared to meet us on the level of rational argument, but begin by denouncing all argument; they may forbid their followers to listen to rational argument, because it is deceptive, and teach them to answer arguments by the use of their fists or pistols. We should therefore claim, in the name of tolerance, the right not to tolerate the intolerant. We should claim that any movement preaching intolerance places itself outside the law and we should consider incitement to intolerance and persecution as criminal, in the same way as we should consider incitement to murder, or to kidnapping, or to the revival of the slave trade, as criminal."[0]

The form of "intolerance towards the intolerant" he actually discusses in his essay is rather far removed from the sweeping authority to suppression that it bestows in the eyes of many of the people who invoke it. He does not recommend censoring or removing any liberties of the intolerant, unless and until they respond to rational argument by force. Unless they instruct followers to disregard rational argument as itself deceptive. Unless they are inciting actual criminal activity.

The idea that some ideas are in and of themselves too dangerous to allow to exist in the public domain, that rational argument should be monitored, controlled, and suppressed to ensure that "tolerance" remains is nowhere to be seen. It is only when the methods of a liberal democracy (that is, open conversation, debate, the marketplace of ideas) fail catastrophically that Popper sees the need for open intolerance towards those who answer argument with violence.

In fact, the argument of the "paradox of tolerance" is actually, you may be surprised to learn, an argument in favor of autocracy. Its whole point is that liberal democracies can't sustain themselves without a "benevolent despot". Popper was arguing against that idea. Per Wikipedia, again; "In the context of chapter 7 of Popper's work, specifically, section II, the note on the paradox of tolerance is intended as further explanation of Popper's rebuttal specific to the paradox as a rationale for autocracy: why political institutions within liberal democracies are preferable to Plato's vision of despotism, and through such institutions, the paradox can be avoided. Nonetheless, alternative interpretations are often misattributed to Popper in defense of extra-judicial (including violent) suppression of intolerance such as hate speech, outside of democratic institutions, an idea which Popper himself never espoused."

[0]: https://en.wikipedia.org/wiki/Paradox_of_tolerance