Anytime someone brings up paradox of intolerance in the fediverse, the chance is very high they're completely wrong about it and are regurgitating shit they read from some dumbass on social media.

1. The paradox of intolerance is a paradox, not a conclusion.
2. The reductive conclusion social media dumbasses insinuate by invoking it is entirely wrong according to the philosopher who articulated the paradox.
3. Intolerant carries a more technical meaning in philosophy (at least to that philosopher) than a mere disagreement with other ways: it includes the element of imposing (by unjustified force) on society to literally prohibit other ways. People who do not force us to comply with their position are tolerant.

From the article (you didn't read or understand) quoting Karl Popper (extended with the rest of the passage)

[Less well known 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 [intolerant ideologies] 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.

The type of intolerance they refer to is the kind that uses force and refuses debate. They even explicitly reject that we should in general "suppress the utterance of intolerant philosophies" as long as rational argument & public opinion still govern public choice.

background: book promotes intellectual freedom

The quote comes from a footnote in the book The Open Society and Its Enemies, whose thesis is that an open society (ie, liberalism) has stronger merits than the newer, trendier totalitarian political theories of the day predicated on teleological historicism. They approached this from their background in philosophy of science (emphasizing enterprises controlled by skepticism and free inquiry) to argue that liberal democracies are not inevitably doomed by totalitarian systems of power, because liberal institutions have an overlooked strength

Only democracy allows an institutional framework that permits reform without violence, and so the use of reason in political matters

and to keep totalitarian systems like fascism or communism at bay, we need to sustain institutions that allow for open inquiry and grant all citizens extensive rights against their governments.

Even with the best rulers, unchecked power is likely to err and cause unbound damage. Instead of focusing only on selecting the best rulers, a better system of government might determine

How can we so organize political institutions that bad or incompetent rulers can be prevented from doing too much damage?

They resolved that such a system should include strict limits on the power of the state and a special emphasis on intellectual freedom.

They were absolutely arguing in favor of more open discourse & deliberation, not less of it, to reform government without violence and restrict its potential damage. That means tolerating opinions we disagree with from people who don't try to impose them with force.

Their discussion on public policy has no bearing on the democratic consequences accepting code that "solves the problem" from people we disagree with. It's pretty much accepting charity and doesn't imply you promote or agree with their views at all. Philosophers generally scoff at purity policing bullshit and genetic fallacies, especially those who emphasize free, open inquiry and rational argument as crucial to an open society.