It's still argument from authority when you use quotations, you know, but I actually don't think Feynman was right about this one -- or rather, I think the context in which he made those remarks is sufficiently different from our own to warrant pause in taking them wholly to heart, as we have effectively done in outreach for many years. We've been so careful to note our uncertainty that we've forgotten to explain how limited our uncertainty is and by extension how confident we really are, and I think that's helped to erode confidence in our institution -- or at least made it easier for the anti-science movement to muddy the waters.
There's a story I like to tell about this involving a guy who, one morning on the bus I was taking to my grad school lab, attempted to convince me that π is exactly equal to 3, as implied by the Bible (1 Kings 7:23). I pointed out that π is demonstrably not exactly equal to 3, and his response has stuck with me: "Scientists have wasted billions of our tax dollars trying to find π, and millions of digits later they still don't have an exact number, just a lot of blather about how it's infinite or whatever. So how can you tell me it's not 3 when you don't know what it is?"
That was an extreme example (and wrong in every particular), but the basic pattern holds from climate change denialism through "citizen science" tomfoolery on into crystal healing woo: we do an absolutely execrable job of explaining how uncertainty actually works for us. We say we can never be absolutely sure about anything and people hear that we have no idea regardless of our actual margins of error; we're so careful to express humility and not sound overconfident that we forget to mention how much we actually know, and that's how the woo-peddlers and Republicans get a chance to spread their nonsense. We've overcorrected relative to 1974, I think.