Re: lumpenproletariat. A possibly misplaced attempt to exaggerate the views to make the differences clearer, I could have said proletariat and it could have been more accurate.

the idea that the "safe speech" people wish to use legal means doesn't really hold very strongly

Why not? In the USA it may appear that way because the first amendment is such a strong protection, so they end up using approaches that aren't based on changing the law (e.g. pushing for corporate censorship policies on large communication services).

But everywhere else in the world doesn't have the first amendment and there you see a proliferation of hate speech laws and other "crimes" that boil down to offending people on Twitter. In the UK the police arrest tweeters so actively that it's become a rolling criticism of the force, like, why are they arresting people who are just sitting on their ass tweeting instead of going out and catching "real" criminals? Answer: because the law expects them to.

What precisely makes you categorise the idea of "there will always be poor people" necessarily in with "free speech advocates"?

Because policy positions follow logically from the underlying intuition about human nature.

Let's start with the assumption that the existence of poverty is a problem. Sowell didn't use the term "free speech" vs "safe speech", he coined the terms constrained vs unconstrained instead. People with the constrained vision look at poverty and agree that it's a problem, but disagree that there's any solution. They see the world as offering only tradeoffs. We could raise taxes and redistribute to the poor through welfare (making poverty better), but that might discourage them from working and reduce the tax base as a whole (making other government services worse). They see hateful or offensive speech and maybe they agree that is a problem, but doing anything about it would only create bigger problems elsewhere. Thus "free speech" types tend to default to a position of inaction or leaving things alone, i.e. shrink the state (less action), if something is traditional best to keep doing it (don't change things), etc. Hence the description 'conservative'.

People with the unconstrained vision see a problem like poverty, but are sure there must be solutions out there, if only the right people can be found and put in power. They therefore spend a lot of time worrying about whether politicians are good people, moral people, they tend to suggest solutions like "tax the rich, feed the poor" and don't worry too much about possible negative side effects: if they acknowledge such side effects might exist at all, their view is usually that these effects are small and controllable, and at any rate, such worries should not stand in the way of experimentation and progress.

are you familiar with the works of the Frankfurt School of critical theory?

Those people who looked at Marxist philosophy and concluded communism was just a bad implementation, not that the outlook on humanity itself was flawed?

I haven't read much by the Frankfurt School, although I have studied what Marx himself believed somewhat extensively (well, relative to most people I guess). Marxist thought is such a nonsensical set of beliefs that anything derived from it is likewise guaranteed to be nonsense, so there are limits to how much time I want to spend on that.

Marx wasn't completely self consistent over time, but in the Sowellian framework of visions, Marx was one of the rare people who had an entirely and utterly unconstrained view of human nature. He believed literally all flaws of human nature stemmed from capitalism ("alienation") and if institutions and markets were abolished, problems like people wanting more than their fair share would disappear as well. That's why he was stupid enough to believe that the "dictatorship of the proletariat" was both (a) not a self-contradicting concept and (b) would simply wrap itself up and dissolve itself once its redistributive work was done.

The naivety about how people really are that's required to believe that could only come from someone living Marx's entirely cloistered life - any school of thought that descends from it deserves no respect.