Consider "Elaine is a post-utopian and the Earth is round" This statement is meaningless, at least in the case where the Earth is round, where it is equivalent to "Elaine is a post-utopian." Yet it does constrain my experience, because observing that the Earth is flat falsifies it. If something like this came to seem like a natural proposition to consider, I think it would be hard to notice it was (partly) meaningless, since I could still notice it being updated.

This seems to defeat many suggestions people have made so far. I guess we could say it's not a real counterexample, because the statement is still "partly meaningful". But in that case it would be still be nice if we could say what "partly meaningful" means. I think that the situation often arises that a concept or belief people throw around has a lot of useless conceptual baggage that doesn't track anything in the real world, yet doesn't completely fail to constrain reality (I'd put phlogiston and possibly some literary criticism concepts in this category).

My first attempt is to say that a belief A of X is meaningful to the extent that it (is contained in / has an analog in / is resolved by) the most parsimonious model of the universe which makes all predictions about direct observations that X would make.