Solipsism is fundamental to any rational belief system

Using solipsism as a standard of confidence is important when measuring rational justification for all other beliefs because it is the only true and objective standard available. It does not follow, as you seem to suggest, that all beliefs are equally justified or unjustified when compared to solipsism. Solipsism is derived from rational inquiry and it follows that other beliefs derived from rational inquiry are more likely to be accurate than beliefs that are not bound by formal logic. A naive realist can hold any number of superstitious beliefs that may or may not be falsifiable without ever considering solipsism. Therefore solipsism is not prerequisite to unfalsifiable beliefs. Specific claims of conspiracy theories and pseudoscience are very likely to be falsifiable and even if they are not falsifiable it does not mean they are necessarily false. Unfalsifiable claims are merely dubious if clearly faith based or lacking direct evidence such as in the classic example of the proposed tea pot in orbit around the planet Mars. Denialism is not dependent on solipsism in any way. The ability to deny any particular evidence as a way to avoid a psychologically uncomfortable conclusion requires no rational logical analysis whatsoever and this can be accomplished without any reference to solipsism. Denialism requires no justification whatsoever and is more of a knee jerk reflex than a justifiable rational belief. So you might ask, how do we know what we know? Well, contextualism seems to leave enough room for elements of empiricism, idealism, rationalism, scepticism, phenomenalism, reliabilism, coherentism, hedonism, utilitarianism and scientism. The more of these that apply to your belief, the more rationally justified your belief is. But if you don't begin your analysis with solipsism, you aren't digging deep enough. Your objections to solipsism seem to hinge on conflating skepticism with a paralyzing lack of confidence. There are many levels of justifiable confidence based on both the amount and logical consistency of evidence available for any particular belief. I hold some beliefs with a high (but not unassailable) level of confidence and others with a medium or lower level of confidence. There are some beliefs I am highly skeptical of but do not qualify as provably false and there are also beliefs I categorize as logically incoherent and still others that are provably false. I offer an example of a general forced to make critical decisions in the fog of war. He may not know exactly how many enemy forces there are and he may not know exactly where they are but this lack of certainty is not paralyzing. The general takes a calculated risk and commands his forces based on what is deemed to be the best evidence available at the moment. He might order more reconnaissance, but by the time that information arrives, the situation will have likely changed once again. If the general naively believes perfect confidence is justified he is more likely to commit too many forces to a single action, risking disaster if his intelligence is outdated or inaccurate. My point here is that you have to know how much confidence is justified in order to mitigate risk. If you treat confidence like a toggle switch, either on or off, you are likely to be alternatively paralyzed and overconfident. If you're trying to say that the assertion "life is but a dream" trumps all rational analysis, I would have to disagree with your position. To borrow from your examples, even if I am willing to grant the premise that my experience is currently part of a dream, there is still evidence within that dream that the United States exists and that other geographical locations beyond the United States also exist. The possibility that your current experience may be a dream does not automatically level the field for all logical and illogical beliefs. Also it seems appropriate to note that it is possible for a conspiracy theory or pseudoscientific claim to be true even if a specific claim lacks compelling and coherent evidence. A poor argument is only evidence of a poor argument, it is not evidence that the claim is in fact false. Although the burden of proof would seem to be generally on the claimant challenging the status quo. And even though personal opinion and anecdotal evidence are not rigorous or scientific, they may still be considered compelling to certain sympathetic audiences and yet they are still not rationally justified. In order to properly gauge your level of justified confidence in any particular belief it is important to keep in mind a benchmark for truth ranging from unquestionably true to absolutely false. "Cogito ergo sum" represents one end of this scale and "1+1=6" lies somewhere on the other end.