looking at the human condition, I see plenty of data to the opposite.

I see it too - but you're only talking about the present. Put it into historical context and it indicates the opposite of what you think it indicates. The history of bullshit is that, while there is still too much of it, it started at vastly worse premodern levels that were really weird, and has been losing arguments ever since.

One of my favorite examples is the reports of the first Protestant ministers who went through the 16th century villages, talked to peasants about what they actually believed and, because they weren't evaluating their own work, actually recorded that. Turns out even after hundreds of years of Catholicism, these peasants had all sorts of ideas, and those ideas varied wildly from village to village or person to person. They'd have three gods, or eight, or even believe in forms of reincarnation. The Protestants went to homogenize that, of course, and in places like Brazil they still do. But even in Europe and the US, the number of distinct belief systems continues to decline.

Far from creating one shared space, today's interconnectivity seems to have led to a bunch of echo-chamber bubbles

Medieval villages and similarly unconnected societies are echo-chamber bubbles too. So the number of bubbles has been going down, sharply, and competition between ideas has clearly become tougher. If an exception like Homeopathy is growing, that means it has been unusually successful in the harder environment (a big part, in this case, was greatly reduced claims of effectiveness). But that shouldn't distract from the fact that lots of pseudotherapies that were comparable to it fifty years ago, such as Anthroposophic medicine and Orgone therapy, have gone down. And of course the quacks and witch doctors that we used to have before those were even more heterogenous and numerous.

And that's exactly what you'd expect to see in a world where whether someone accepts an idea very much depends on what else that someone already believes. People aren't usually choosing rationally what to believe, but they're definitely choosing.

There seems to be a hard-coded exception for young kids, who will believe any bullshit their parents tell them, and that, rather than active conversion, is how some religions continue to grow. Surely it also helps bullshit that isn't religion.

I'm obviously not doing this experiment you're talking about, because it is wildly unethical and incurs severe social cost. And even if it turned out I can convince people of bullshit just as well as I convince them of rationality, that wouldn't be relevant to my original assertion that convincing the unconvinced is not at all an "open and hard problem".