I don't think having beliefs about "pure democracy", "pure capitalism" or "pure communism" are very useful for making political decisions. In the real world our systems aren't pure but very complex systems.
For signaling tribal alliance it's okay to speak in favor of "pure X" but it's not good for driving any kind of political agenda. Putting a probability on whether or not "pure democracy" is good doesn't help with the core issue.
You don't want to have a state where the only way to change the government happens to be a coup d'état because that way to change your government is much more expensive than holding elections.
You want to have public discussion that can affect public policy that's open to people who are willing to engage with public policies.
It's been a while since I read Rousseau but if I remember correctly for him democracy was simply a state where the government does what's in the interest of the people and not necessarily what the people say when you ask them.
If power is concentrated on few people that doesn't happen for the reasons Bruce Bueno de Mesquita described in the Dictator's Handbook and as a result it makes sense to design a system in a way that spreads power over more people.
Representative democracy is a tool to spread out power. Thinking of it as a tool that's supposed to translate public opinion as directly as possible into public policy misunderstands it's core purpose.
Going deeper into understanding a purpose helps to develop positions that aren't "20% that pure democracy is good" and "80% that oligarchy is good" but that have a different structure.
You could try to bite bullets and believe the inconvenient facts.
You could try to find the facts and change your politics to fit.
You mention that you "feel committed to the last". If you had used the word "beliefs" instead of "politics," I would endorse and agree with your commitment. Given that you used the word "politics," though, I'm inclined to believe that the better path is somewhere between the two positions quoted above.
I agree that "[for] almost any political position, there is at least one inconvenient fact." (Or, at least, I think I agree; I think that you are using the terms "political position" and "inconvenient" in the way that is intuitive to me.) But political positions are only sufficiently powerful enough to enact change when multiple people believe in them, or believe in something close enough that they can work together. There are inconvenient facts that I'm aware of which cast doubt on some of my political positions, but the doubts are small enough that I believe it better to hold onto the imperfect position than to abandon it. Politics is not a game of finding optimum solutions; it is a game of coalition-building, of incremental change, of pushing for policies that are better than what existed before. (I would imagine that this fact is part of the source of the frustration many aspiring rationalists feel toward politics. I know that I feel this frustration.)
So let's set aside politics for the moment, because you seem to use the term roughly interchangeably with "belief", e.g. "whatever you wish to believe, there is, somewhere, a fact that will cast doubt on it."
But my beliefs are probabilistic in nature. Seemingly contradictory facts are not enemies -- to the contrary, they are expected. If I believe that a die is weighted such that the number six will show up 25% of the time, I will bet on each roll coming up on six. 75% of the time, the facts will appear to be against me -- and yet, if I bet at the right odds, I'll still expect to win in the long run. It is my intuition that this stance lies closer to "[trying] to bite the bullets and believe the inconvenient facts" than "[trying] to find the facts and [changing] my [beliefs] to fit."
Of course, I should still update the probability based on each roll I see, so maybe that counts as "[changing] my [beliefs]"? I'm not sure. Maybe my point is just that I'm not clear on what difference you're making between those two options. Really, your first option, "[taking] a stance of strong epistemic and moral modesty, and never [taking] a position with confidence," could also describe the situations I touched on above.
When I say "your politics", I mean something composed of several related beliefs, entangled with culture, values, judgments about the best policy, and, usually, tribal affiliation and sense of identity. I could also say "memeplexes", possibly, but that would include some things I don't think it applies to, like Empiricism.
What are your politics?
What frameworks have you acquired for structuring your interaction with the world?
What facts support them?
What possibilities would undermine them? What significant counterexamples could exist, and which of them could prove to be fact?
If there were a verb meaning "to believe falsely," it would not have any significant first person, present indicative.
I assert that this is not as true as it seems. Yes, few if any people are willing or able to admit that they hold any specific false belief. If you don't count beliefs in belief or aliefs, it's speculative whether it's logically possible. But I, for one, do believe falsely. I falsely believe something. I am quite sure of it.
The world is wide, and beliefs are complex. Systems of beliefs, like politics, ideology, frameworks, even more so. A complex set of beliefs has many premises it rests on; perhaps none is individually a crux, but propositions that, if false, would cast the rest into doubt in a serious way.
And because there are so many, it is extremely likely, near-certain, that at least one of them is wrong. For almost any political position, there is at least one inconvenient fact.
You may not know it. Perhaps it turns out that, contrary to your ideals of rational actors and self-determination, people born with strawberry-blonde hair are inherently dangerously biased toward pyromania and risk-seeking behavior that they do not endorse, and no one has proposed this, let alone investigated it. Maybe there is a curiously-specific unified field theory that proves that blue is the best color.
But somewhere, the fact is out there. The world is not politically convenient; whatever you wish to believe, there is, somewhere, a fact that will cast doubt on it.
So what should you do?
You could take a strong stance of epistemic and moral modesty, and never take a position with confidence.
You could reject it and embrace views you know are probabilistically ill-founded.
You could try to bite bullets and believe the inconvenient facts.
You could try to find the facts and change your politics to fit.
As a rationalist, I feel committed to the last. I have had some success, but I don't truly believe there are no remaining inconvenient facts. If I'm lucky, it is something that suits my less-endorsed instincts, like an elitist "pure democracy and sane government are fundamentally incompatible" that pushes in the direction of something possibly palatable like oligarchy. If I'm less lucky, it's something like "the CEV of humanity includes only very small terms for intellectual exploration".
But in any case, I think it would benefit everyone, in political and cultural arguments, to remember that somewhere, the Inconvenient Fact exists. For every position modern humans hold, there is some fact that calls it into question. This is true for your opponents and also for you.