Only ironic if you take it out of context:

    BARSAMIAN: ....You're very patient with people,
    particularly people who ask the most inane kinds of
    questions. Is this something you've cultivated?

    CHOMSKY: First of all, I'm usually fuming inside, so
    what you see on the outside isn't necessarily what's
    inside. But as far as questions, the only thing I ever
    get irritated about is elite intellectuals, the stuff
    they do I do find irritating. I shouldn't. I should
    expect it. But I do find it irritating. But on the
    other hand, what you're describing as inane questions
    usually strike me as perfectly honest questions. People
    have no reason to believe anything other than what
    they're saying. If you think about where the
    questioner is coming from, what the person has been
    exposed to, that's a very rational and intelligent
    question. It may sound inane from some other point of
    view, but it's not at all inane from within the
    framework in which it's being raised. It's usually
    quite reasonable. So there's nothing to be irritated
    about.

I basically read that as:

    Interviewer: Do you get angry when people ask you inane
    questions?

    Chomsky: Only when the person asking it should know
    better.

Whether or not Chomsky and the interviewer's idea of what constitutes an inane question is the same as mine or yours may be grounds for criticism. But just quoting the bit that you did out of context is dishonest, and definitely fits with my idea of what constitutes an inane comment.