From an interview with Rabbi Hershel Schachter (original missing):
If the posek knows that the person asking will not be able to follow a machmir pesak and will get frustrated and give up on his Jewish observance, he cannot say that what he is asking for is absolutely asur. He has to show him that there are different positions in Halachah on the issue and remind him that by following the more lenient opinion he is still acting within the halachic framework. We believe that eilu va-eilu divrei E-lohim Chayyim (these and those are the words of the Living God) is a halachic principle and that bi-she’as ha-dechak (in extremis) you can rely on the shittah ha-mekilah (lenient opinion).
If you can’t wake up the Jew’s Fear/Love, perhaps its enough to give a cryptic answer, so the questioner bears the blame for his own decision? Or to send him to ask someone else? Either way, he’s still within the so-called “halachic framework”, but you haven’t made halacha into a joke…
And besides, “Elu Va’elu” doesn’t always apply; sometimes both positions are incorrect, or only one is correct. And it is no sort of “halachic principle” (at least until the Achronim)!
See what we wrote about Elu Va’elu here before.
Disclaimer: Never trust anonymous articles on the internet.
Update: Rabbi Schachter was more clear over here; “Elu Va’elu” does not include mistaken views.