"Rationality" leads people to believe such absurd ideas

Are you sure you have pinpointed the right culprit? Why exactly "rationality"? "Zooming in" and "zooming out" would lead to potentially different conclusions. E.g. G.K.Chesterton would probably blame atheism[1]. Zooming out even more, for example, someone immersed in Eastern thought might even blame Western thought in general. Despite receiving vastly disproportionate share of media attention it was such a small part of LessWrong history and thought (by the way, is anything that any LWer ever came up with a part of LW thought?) that it seems to wrong to put the blame on LessWrong or rationality in general.

Furthermore, which would you say is better, an ability to formulate an absurd idea and then find its flaws (or, for e.g. mathematical ideas, exactly under what strange conditions they hold) or inability to formulate absurd ideas at all? Ability to come up with various absurd ideas is an unavoidable side effect of having an imagination. What is important is not to start believing it immediately, because in the history of any really new and outlandish idea at the very beginning there is an important asymmetry (which arises due to the fact that coming up with any complicated idea takes time) - an idea itself has already been invented but the good counterarguments do not yet exist (this is similar to the situation where a new species is introduced to an island where it does not have natural predators, which are introduced only later). This also applies to the moment when a new outlandish idea is introduced to your mind and you haven't heard any counterarguments by that moment, one must nevertheless exercise caution. Especially if that new idea is elegant and thought provoking whereas all counterarguments are comparatively ugly and complicated and thus might feel unsatisfactory even after you have heard them.

the presence of a significant number of people psychologically affected

Was there really a significant number of people or is this just, well, an urban legend? The fact that some people are affected is not particularly surprising - it seems to be consistent with the existence of e.g. OCD. Again, one must remember that not everyone thinks the same way and the common thing between people affected might have been something other than acquaintance with LW and rationality which you seem to imply (correct me if my impression was wrong).

the fact that Eliezer accepts that basilisk-like ideas can be dangerous

I think it is better to give Eliezer a chance to explain himself why he did what he did. My understanding is that whenever someone introduces a person to new variant of this concept without explaining proper counterarguments it takes time for that person to acquaint themselves with them. In very specific instances that might lead to unnecessary worrying about it and potentially even some actions (most people would regard this idea as too outlandish and too weird whether or not it was correct and compartmentalize everything even if it was). A clever devil's advocate could potentially come up with more and more elaborate versions of this idea which take more and more time to take down. As you can see, it is not necessary for any form of this idea to be correct for this gap to expand.

Personally I understand (and share) the appeal of various interesting speculative ideas and and the frustration that someone thinks that this is supposedly bad for some people, which seems against my instincts and the highly valuable norm of free marketplace of ideas.

At this point in time, however, the basilisk seems to be more often brought up in order to dismiss all LW, rather than only this specific idea, thus it is no wonder that many people get defensive even if they do not believe it.

All of this does not touch the question whether the whole situation was handled the way it should have been handled.

[1] Although the source says that famous quote is misattributed. Huh. I remember reading a similar idea in one of "Father Brown" short stories. I'll have to check it.

(excuse my english, feel free to correct mistakes)