If a philosophical framework causes you to accept a basilisk, I view that as grounds for rejecting the framework, not for accepting the basilisk. The basilisk therefore poses no danger at all to me: if someone presented me with a valid version, it would merely cause me to reconsider my decision theory or something. As a consequence, I'm in favor of discussing basilisks as much as possible (the opposite of EY's philosophy).

One of my main problems with LWers is that they swallow too many bullets. Sometimes bullets should be dodged. Sometimes you should apply modus tollens and not modus ponens. The basilisk is so a priori implausible that you should be extremely suspicious of fancy arguments claiming to prove it.

To state it yet another way: to me, the basilisk has the same status as an ontological argument for God. Even if I can't find the flaw in the argument, I'm confident in rejecting it anyway.