Everyone (and every group) thinks they are rational. This is not a distinctive feature of LW. Christianity and Buddhism make a lot of their rationality. Even Nietzsche acknowledged that it was the rationality of Christianity that led to its intellectual demise (as he saw it), as people relentlessly applied rationality tools to Christianity.

My own model of how rational we are is more in line with Ed Seykota's (http://www.seykota.com/tribe/TT_Process/index.htm) than the typical geek model that we are basically rational with a few "biases" added on top. Ed Seykota was a very successful trader, featured in the book "Market Wizards" who concluded that trading success is not that difficult intellectually, the issues are all on the feelings side. He talks about trading but the concepts apply across the board.

For everyone who thinks that they are rational, consider a) Are you in the healthy weight range? b) Did you get the optimum amount of exercise this week? c) Are your retirement savings on track? d) Did you waste zero time today? (I score 2/4).

Personally I think it would be progress if we took as a starting point the assumption that most of the things we believe are not rational. That everything needs to be stringently tested. That taking someone's word for it, unless they have truly earned it, does not make sense.

Also: I totally agree with OP that it is routine to see intelligent people who think of themselves as rational doing things and believing things that are complete nonsense. Intelligence and rationality are, to a first approximation, orthogonal.