I find the idea that we no longer live in "an era where many of our ideas about the world [are] fundamentally wrong" quite amusing. It's not even been twenty years since the UK's leading medical institutions were thoroughly convinced that vaccines caused autism. Not through epistemological anarchism, but through good ol' numbers fudging, conclusion skewing and mass media induced panic, in serious-looking, play-by-the-numbers-seeming research papers.
The way you tell "epistemologically anarchist theories" from quackery is the same way you tell any other theories from quackery: you test them.
The way you tell "epistemologically anarchist theories" from quackery is the same way you tell any other theories from quackery: you test them.