I'll further argue that the Paradox of Intolerance, used in this instance, implies that if we do not tolerate intolerance we can effectively snuff it out or meaningfully prevent it and thus we do not have to tolerate intolerance at all. The sad fact is that that is not true unless you are willing to cull opposing opinions

That is exactly what is necessary, to snuff out intolerant voices as the one thing the tolerant must do. Opposing opinions is what they claim to be, but the intolerant hate spewers isn’t about opposing opinions at all, it’s rather “you are not entitled to your opinion”. It’s a false equivalency that allows intolerant to gain an advantage because they do not play by the same rules or definitions. The whole moving goalposts strategy for instance.