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.