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.

To the contrary, lots of groups make a big point of being anti-rational. Many groups (religious, new-age, political, etc.) align themselves in anti-scientific or anti-evidential ways. Most Christians, to make an example, assign supreme importance to (blind) faith that triumphs over evidence.

But more generally, humans are a-rational by default. Few individuals or groups are willing to question their most cherished beliefs, to explicitly provide reasons for beliefs, or to update on new evidence. Epistemic rationality is not the human default and needs to be deliberately researched, taught and trained.

And people, in general, don't think of themselves as being rational because they don't have a well-defined, salient concept of rationality. They think of themselves as being right.