OK, the Paradox of Tolerance is a Karl Popper social theory about how society should feel about its subgroups, and made recently famous again in a comic, although I don't think the comic context is relevant to this meme.

The basic idea is that if we tolerate absolutely every subgroup, then we are logically also tolerating the existence of fascists and other types of subgroups that want or promote intolerance. If one of these groups (let's say, Nazis) is tolerated by society, it may gain control--indeed, to Popper, this is inevitable--and society becomes intolerant again. So paradoxically, tolerating everything led to the collapse of tolerance itself.

His remedy is that we must not tolerate the intolerant, we must extinguish groups like that through various means. To be clear, Popper is NOT saying we must kill or commit violence against the members of those groups, just that we must make sure the group structure itself is dismantled as it's being built in every case. And here we get to the rather terrible point being made by the meme. "Minorities", as the meme puts it, would be the Nazi group from the earlier example, because their viewpoint is a minority. And Popper isn't promoting violence against them, unless you consider the enforcement of laws to be inherently violent. (A valid point of view, but very far from what the meme is suggesting.)

The paradox of tolerance isn't a paradox. This meme's body says "Tolerance is not a moral precept - Yonatan Zunger", which essentially means that tolerance isn't a fundamental moral belief, it springs forth from other beliefs and because of that is not absolute. The meme itself is saying that arguments that use the paradox of tolerance are just a proxy, that what the person using the argument is trying to argue for is that people should be ok with their bigotry. How I personally conceive of tolerance is that it's a social contract, where if one side chooses to break the contract then the other side no longer has to obey it either.

My take is that instead of being intolerant of intolerance (the paradox), they want to be an edge lord sack o' shit and be intolerant of things other than intolerance. "To be cool."

Yep. The idea of a paradox of tolerance is that, if you believe tolerance to be a moral precept, then you inherently will be tolerating others intolerant actions, speech, etc. Not sure why this is a thing, unless it’s meant to dunk on the idea that people should strive for being tolerant of others.

That said, the article is correctly pointing out that tolerance is not a moral precept, but rather a social contract To exercise tolerance need not implicitly accept intolerant behaviors of others. Intolerance exhibited from others is a break in such a contract. The contract requires willing participants in tolerance.

Agreed