I found a statement by Steven Pinker to an Argentine newspaper that in my opinion can not be more consistent with the issues expressed by Herbert. In his last TED talk Pinker affirmed that "We will never have a perfect world, and it would be dangerous to seek one", about which he expanded:
We are not clones. There are biological and cultural variations and that is why there are always going to be mutual concessions between
freedom and equality. If you treat people equally, they will end up
being unequal. Some people are smarter than others, work more, take
more risks or have more luck. The only way that people end up being
equal in the result, is if you treat them in an unequal way. Freedom
and equality have mutual concessions. You can not have much of both.
Freedom also has concessions with human development. If you give
people freedom, they can do stupid things like eating a lot, taking
drugs, not exercising or dealing with unpleasant ways. If you force
everyone to do what is best for them and everyone else, you would need
a totalitarian Big Brother. There are concessions between the good
things of life and human freedom. The people who would form the
society that would try to be perfect are also human, with the flaws
that accompany human nature. They would be tempted all the time to
abuse their power and overestimate their knowledge. They might think
that they know how to create a perfect society and we know that humans
have a lot of confidence in their knowledge. They would be tempted to
impose a vision on society that might not benefit everyone.
Inside that quote there is also sentences besides equality that can be close compared with other hot topics in Herbert books. "They would be tempted all the time to abuse their power" can be compared with:
“All governments suffer a recurring problem: Power attracts
pathological personalities. It is not that power corrupts but that it
is magnetic to the corruptible.” -F. Herbert, Chapterhouse: Dune
And "If you give people freedom, they can do stupid things" compared with:
“Seek freedom and become captive of your desires. Seek discipline and
find your liberty.” -F. Herbert, Chapterhouse: Dune
So, at least in these topics, I think his points of view seems very close.
Besides, I managed to found a 1981 interview at Mother Earth News, an ecology-oriented magazine, that think could be relevant to navigate his political thinking outside his books. There you could find his opinion about the welfare state:
I don't like governmental "helping"—or any kind of public charity
system—because I learned early on that our society's institutions
often weaken people's self-reliance and damage family bonds as well.
Or about leaders, in his views on Kennedy and Nixon:
There is definitely an implicit warning, in a lot of my work, against
big government and especially against charismatic leaders. After all,
such people—well-intentioned or not—are human beings who will make
human mistakes. And what happens when someone is able to make mistakes
for 200 million people? The errors get pretty damned BIG!
For that reason, I think that John Kennedy was one of the most
dangerous presidents this country ever had. People didn't question
him. And whenever citizens are willing to give unreined power to a
charismatic leader, such as Kennedy, they tend to end up creating a
kind of demigod—a leader who covers up mistakes instead of admitting
them—and makes matters worse instead of better. Now Richard Nixon, on
the other hand, did us all a favor.
Nixon taught us one hell of a lesson, and I thank him for it. He made
us distrust government leaders. We didn't mistrust Kennedy the way we
did Nixon, although we probably had just as good reason to do so. But
Nixon's downfall was due to the fact that he wasn't charismatic. He
had to be sold just like Wheaties, and people were disappointed when
they opened the box.
I think it's vital that men and women learn to mistrust all forms of
powerful, centralized authority. Big government tends to create an
enormous delay between the signals that come from the people and the
response of the leaders. [...] The bigger the government, the more
slowly it reacts. So to me, the best government is one that's very
responsive to the needs of its people. That is, the least, loosest,
and most local government.
His dislike of centralized government and social aid makes me think that the equality he advocates is that of a social anarchism. He seems to be against affirmative action as a way to equalize people's equality of opportunity. But if after all this reading you find it difficult to classify his political ideas, don't feel bad. The interviewer Pat Stone himself stated:
Throughout this interview it's been all but impossible to pin you down
to "neatly packaged" ideas. [...] I can imagine that many men and women who
read your books or hear your ideas would prefer to be given a clear
and uncomplicated plan they could respond to.
PS: I apologize to answer my own question, but I really needed to research about this, and used all the precious insights shared in the discussion to do it.