First, I don't hate Star Trek: Deep Space Nine. I think it is very well acted. Much of it is well-written. Many of the things I dislike about it I dislike in retrospect because the creators of ‘New Trek’ have chosen to accentuate them or make them the focus of entirely new plots. This is not entirely fair to Deep Space Nine. Its faults are faults, but its writers weren't the ones who decided to turn one of them into a spinoff series.
But, my thesis is that DS9's flaws stem from it being, perhaps unintentionally, a critique of Star Trek from the Right.
This doesn't mean, incidentally, that I think only left wing science fiction is legitimate or enjoyable, I've read many Heinlein books and enjoyed the ones that don't have sex cults in them. It is the case that Star Trek, however, has by its nature from the beginning been specifically progressive, and many people who argue that it should continue to be don't seem to notice these examples of it conspicuously failing to be.
It has been said that it is easier to imagine the end of the world than to imagine the end of capitalism. Star Trek may not have had the most realized version of this (they are very obviously centrally planned to heck and back but people at least seem to have the chance to do things that they really enjoy doing in good conditions.) but they did it. Deep Space Nine asks, “What? A world without capitalism? Be serious!”
You mostly see it in Quark's, as said before the economy of the Federation has been, at best, a vague sketch, but gone is recreation as a public good, with people having to find latinum somewhere if they want to carouse in a bar or lounge, visit a holosuite, or play a game of Parrises squares.
But there is one quote that is capitalist apologetics per se:
Quark: The way I see it, Humans used to be a lot like Ferengi: greedy, acquisitive, interested only in profit. We're a constant reminder of a part of your past you'd like to forget.
Sisko: Quark, we don't have time for this.
Quark: You're overlooking something. Humans used to be a lot worse than the Ferengi: slavery, concentration camps, interstellar wars. We have nothing in our past that approaches that kind of barbarism. You see? We're nothing like you... we're better.
First, it is my contention that Quark's pants burn with the fires of Hell. Either that or the writer forgot for a moment that they subjugate half their population with women unable to own property and forced to spend all their time naked.
But more importantly, this is the classic bait and switch. The problem isn't capitalism. Workers don't need control of their labor and the means of production. People don't need freedom from domination, they need to be dominated by nice people. it's the same playbook I remember from my youth in the religious right. Every critique of capital was turned into a talking point for Dominionism. Workers unable to afford housing and food for their children? We just need to teach Good, Christian Values in the schools. Horrible workplace safety? That wouldn't happen in a Christian nation.
Marx wasn't right about everything, but he was right that the virtue of individual capitalists was of no account. A capitalist taking a lesser profit to treat workers better will tend to be squeezed out or acquired by someone who doesn't under the coercive law of competition, capitalism optimizes for capital. Bad systems both make (because they see no other choice) and empower bad people.
Surely, not a world without Kissinger?
I hate Section 31. Partly, this is because they're badly written. They're supposed to be diabolically clever schemers supreme waiting in every shadow, and when we actually see them, they're like children playing at being Bond villains.
But that's not the worst of it. The worst is that it's a flat denial of the possibility of an open society accountable to the people. Section 31 is Putin's claim, that there are two types of societies: those run by strongmen and those run by strongmen that pretend not to be, taken to the stars. It's possibly the most reactionary thing ever to be put under the Star Trek name.
People will insist that you can't have a coherent society that defends itself like the Federation without something like Section 31, but that's simply false. You can tell it's false by looking at our own history. Take Kissinger: the only thing he's actually good at is branding. He'll sell you a bill of goods labeled Realpolitik and make the same claims about how he does the things the US needs to do to Survive…
Except…the more classification falls away, the more the leaks come out, the more it becomes obvious his adventurism was the Three Stooges on a murder spree. And that's how it turns out to be with all of this stuff. Every leak, every declassification, is itself just an indictment of classification. The secrecy claimed to be needed to protect the Free People of the World turn outs to be protecting only capitalists selling weapons or looting victims and officials getting high off their own power. This isn't to say that tactics can't be kept secret for a time. I'm not saying that Churchill should have published the complete plans for D-Day in the Times of London, but D-Day became very not secret very quickly once it was executed. Any legitimate secret is short-term and available for the public to see and critique as soon as there isn't an active endeavor involving it. Similarly, this doesn't mean Starfleet Inteligence wouldn't exist, simply that their classified activities would be relatively few and be declassified relatively quickly.
Occasionally someone, channeling their inner Zack Snyder fan, will say “You just don't like Section 31 because you can't handle moral complexity!” This is false. Deep Space Nine actually has examples of moral complexity that are good. Within the framework of a unified polity that can make commitments binding on all its citizens (some people don't accept this as legitimate, which is fine, but it is at least consistent with the Federation as represented. They make treaties.), the Maquis arc involving Eddington is moral complexity that's actually well done.
OOPS! All bigots
The laws stating that genetically engineered people have evil inherent in their biology and must be excluded from society are another plot point I wouldn't be so angry about if they weren't drawn upon in the new series. Similar to the way that Spock's Brain and Turnabout Intruder can be regarded as simply bad episodes because nobody was dumb enough to make them major plot points in every future series going forward.
We're expected to believe that because of Khan Noonien Singh and the Eugenics Wars, the Federation has decreed all genetically engineered people to be Bad. Similar to the way that because of the long history of conflict with the Klingons, everyone in the Federation with any Klingon ancestry is barred from serving in Starf—
Oh, wait. That didn't happen. Because the idea is absolutely inane. How much more inane, then, is the idea that because of a war four-hundred years ago there are laws on the books officially unpersoning people for unchosen modifications to their DNA that don't actually harm anyone? Also, why do any non-Earth Federation members go along with this? Are we to believe that the Vulcans, the Andorians, the Telerites, every other species that doesn't have this trauma in their history are willing to accept a draconian and utterly unjust law because the humans have anxiety over a war from centuries ago?
There is a notion underlying this, and it's telling to me that it's one often articulated by people who defend this bit of world-building as ‘realistic’. it could be summed up well as “Someone has to be oppressed! Just hope it's not you.” I consider this another intensely reactionary concept, largely because neo-reactionaries love invoking it to defend their preferred societal structures.
There are ways one could investigate bigotry within the Federation if one wanted. We see some of it with O'Brien's reference to ‘The bloody Cardies.’ An arc where a civilization with which there have been recent and bitter wars joins the Federation and how people react to and treat them would do just that, and do it well.