If I read you correctly, you're saying that democracy rejects the notion of objective truth. I'm inclined to disagree. Any system of laws seems pretty objective to me.
I do not mean this.
Let's review what democracy requires (a
republic as we understand it imposes additional requirements):
At the bare minimum, we require a system where competing ideas are discussed openly, and then the public picks the ideas it likes best to be implemented.
For this to work, at the bare minimum we must have an environment, secured by law, where people are free to express their opinions to be reviewed by the public.
In any environment where you have two competing ideas, one of them (at the minimum) is wrong. Yet, for democracy to exist, you must secure an environment (by free speech laws and other legal protection) where the people who propose these ideas are free to do so
equally. Your right to express your opinion is equal, regardless of whether you're objectively right. If you persuade the majority of the public, your opinion is usually implemented, even if it is wrong (though in a Republic there are limitations to that).
In fact, even when an idea is rejected by the general public as wrong, its proponents are still free to try and swing the pendulum back again. But the mechanism by which it is done is not rigged to favor some pre-selected notion. (In a Republic, you limit the democracy by various laws that limit the ability of the majority to enforce its will, but that's not the point here.)
