I've spent so much time in the cogsci literature that I know the LW approach to rationality is basically the mainstream cogsci approach to rationality (plus some extra stuff about, e.g., language), but... do other people not know this? Do people one step removed from LessWrong — say, in the 'atheist' and 'skeptic' communities — not know this? If this is causing credibility problems in our broader community, it'd be relatively easy to show people that Less Wrong is not, in fact, a "fringe" approach to rationality.
For example, here's Oaksford & Chater in the second chapter to the (excellent) new Oxford Handbook of Thinking and Reasoning, the one on normative systems of rationality:
Is it meaningful to attempt to develop a general theory of rationality at all? We might tentatively suggest that it is a prima facie sign of irrationality to believe in alien abduction, or to will a sports team to win in order to increase their chance of victory. But these views or actions might be entirely rational, given suitably nonstandard background beliefs about other alien activity and the general efficacy of psychic powers. Irrationality may, though, be ascribed if there is a clash between a particular belief or behavior and such background assumptions. Thus, a thorough-going physicalist may, perhaps, be accused of irrationality if she simultaneously believes in psychic powers. A theory of rationality cannot, therefore, be viewed as clarifying either what people should believe or how people should act—but it can determine whether beliefs and behaviors are compatible. Similarly, a theory of rational choice cannot determine whether it is rational to smoke or to exercise daily; but it might clarify whether a particular choice is compatible with other beliefs and choices.
From this viewpoint, normative theories can be viewed as clarifying conditions of consistency… Logic can be viewed as studying the notion of consistency over beliefs. Probability… studies consistency over degrees of belief. Rational choice theory studies the consistency of beliefs and values with choices.
They go on to clarify that by probability they mean Bayesian probability theory, and by rational choice theory they mean Bayesian decision theory. You'll get the same account in the textbooks on the cogsci of rationality, e.g. Thinking and Deciding or Rational Choice in an Uncertain World.
At the very least crazy ill-thought through knee jerk anticapitalism and anti-nuclear-power irrationality often are "the output of academia". I mean you can take classes in them and everything. ;)
Sure one can cherry pick and say that only this and that part of academia is or isn't trustworthy and deserves or dosen't our promotion of its output, but hey that was my position remember?
Antivaxers irrationality is just garden variety health related craziness which is regrettable since it costs lives but springs up constantly in new forms. Its cost is actually currently pretty low compared to others.
Global warming or at least talking vaguely about "global warming denial" is considered somewhat mind-killing on LW. Also much as with MM I suggest you do a search and read up and participate in previous debates. My personal position is that it is happening yet spending additional marginal effort on solving it or getting people to solve it has negative net utility. Suggest you read up on optimal philanthropy and efficient charity to get a better feeling of what I mean by this.
Theism, meh, I used to think this was an especially dangerous kind of crazy, yet now I think it is mostly relatively harmless compared to other craziness at least in the context of Western cultures. When happy new atheists first stumble upon LW I sometimes find myself in the awkward position of smiling nervously and then trying to explain that we now have to deal with real problems of irrationality. Like society rationalizing death and ageing as something good or ignoring existential risk.