Is the statement "Claims demand evidence" always true?

[Mudhammam]

Because I'm sensitive to context. In the context of living my daily life, I haven't stumbled on a good reason for a solipsistic outlook...
In the context of determining absolute truth, though, all that goes out the window. In context of mundanity, it doesn't MATTER what underlies it all... But by discussing what's outside that context, we are attempting to apply what is experienced to what underlies experience. This seems like a pretty pointless exercise (in a logical sense, not in a pragmatic one).

There are a number of assumptions in here that I find suspect. For example, I'm less inclined to believe that the gulf that separates the two contexts you mention is as great in its disparity or as inconsequential in its impact on action as you imply. This is undoubtedly true to some extent, such as the activities that you would continue to engage in regardless of what underlies appearances, but it seems undeniable to me that what is in fact true about the world, or even merely that which one believes about it, often does influence outcomes, whether the issue exclusively pertains to one's ethical or theoretical outlook. Of course, there's plenty of room for disagreement, but it remains true that progress is possible, which could not be the case if all was subjective.