Well - I'm struggling to understand what your beliefs about the scientific community actually are. You very clearly stated - in no uncertain terms - that the scientific community had significant numbers of crackpots... You're now backing away from this claim... and are now stating that this em-drive situation is just an isolated anomaly from an institutional point of view and that your real frustration is with the untrained public that won't listen to what you say.
Okay - I'm happy to roll whatever direction you're rolling - so long as we signpost the forks in the road clearly along the way. We're no longer talking about professional, institutional crack-pottery - we are talking about the untrained public. Signposted.
I won't abstract away from this particular example just yet - as there is a clear point of dis-analogy between your hypothetical and this em-drive case... in this case there is a prestigious institution backing this research. It is impossible for non-trained people to make an independent assessment of the cost vs benefits of this research. So it's entirely reasonable for them to be interested and excited when they see such an institution running experiments on what otherwise seems like a moonshot.
Even if other institutional voices like yours are arguing against it - in such cases - it's still quite reasonable for a layperson to shrug and say - well, I see the institutional powers that be disagreeing, but the outcome would be so cool if it turns out to be correct. So meh - let's give it a shot.
And I contend that this is an entirely reasonable response of the layperson in this SPECIFIC case. If it turns out to be the case that this was an egregious waste of money, then the public shouldn't be blamed. And if it is also true that this is an isolated case of institutional failure (as you now seem to believe) - i.e. something which was not a result of systemic flaws in the institution of science - then it's just one of those things... a fuck-up that couldn't be helped because you can't control everything in complex science, and giant institutions.
So in THIS case - just chill. It's not a big deal.
Turning to your hypothetical case - which seems to assume that there is no institutional disagreement whatsoever... well that's a different story. Here your frustration with the public is understandable... although I would tend to diagnose that you have a bad habit of taking it out of your colleagues and the public in cases like the em-drive one where they probably don't deserve it. I probably shouldn't have been so hard on you for that - I'm certainly guilty in the past of having been less than generous to my opponents.
So in the interest of all round good mental health - since this is likely the TRUE source of the frustration... perhaps it's worthwhile thinking it over a little bit for both if respective sanities.
Here is what I believe to be the UR-FACT of public/scientific(academic) interaction.
UR-FACT: It is IMPOSSIBLE to communicate modern science to lay people - unless they go through a significant number of the same hoops required to become a scientist.
Let me qualify this. You can communicate its results, models and data in various high level, poetic and metaphorical language. But you cannot communicate it in such a way so as to enable a layperson to examine a particular result and make an independent and accurate judgement as to whether or not that result is true or not... unless you start from scratch and properly induct that person into the institution of science.
I'm not going to argue at length for the UR-FACT unless you challenge me on it. It's prima-facie true.
Let's now evaluate your frustration in light of the UR-FACT. You mention that you are getting frustrated because you have tried "patient explanation", but people still don't agree with you. Well - given the UR-FACT, it's clear that patient explanation was never going to get you anywhere.
So here's a question you need to be asking yourself VERY SERIOUSLY. I'm going to call this question the UR-QUESTION of public/scientific(academic) interaction.
UR-QUESTION: If the public is in general incapable of any genuine understanding of scientific practice as per the UR-FACT, why do scientists (like yourself) take the time out to give ANY sort of explanation at all?
I can't overstate the importance of this question... because if it turns out that there is NO value to this process of engagement between science and the general public, then this has very broad and extreme implications for human progress and its political organisation. If the progress that science makes possible must be protected and if we can't protect this progress through engagement with a democratic polity - then the democratic nature of that polity will have to be eradicated, and the institution of science defended through force.
This would be a nightmarish scenario - so until we are really SURE that engagement has NO value, we had better start coming up with some good models of what the value of that engagement might be, and start applying those models in practice so that we can realise whatever value is there.
But what possible value is there in engagement with the public if it's not to produce understanding?
Here's one possible hypothesis I think is worth considering. Public engagement derives its value not from any understanding it produces, but in the signalling act between scientist and layman.
What do I mean by "signalling act" - well it's a long story. It derives from the concept of signalling in evolutionary biology - which has since been applied to behavioural economics and other domains. The gist is - people employ signals to covertly convey information to other humans about things like status, tribal loyalty, mate fitness and reliability - stuff that was basic to survival back in the day. So we drive fast cars to signal status... we buy expensive rings to signal mate reliability.. etc.
So what is going on then between scientist and layman when they get into arguments about funding priorities in science? If it isn't about actually exchanging understanding, then what explains the behaviour? Why would humans have evolved to waste THAT much time on such a waste of time? The signalling hypothesis suggests that what is going on is a status game between scientist the layperson. The scientist demands to be agreed with - i.e. requests a signal of his/her status, and when the layperson refuses to give that agreement, it is taken by the scientist that their status is being challenged.
Status was important back in the day. Those at the bottom of the tribe status-wise faired poorly. So we evolved psychological mechanisms to motivate us to seek status. That frustration you feel when you "patient explanations" didn't work? That's negative affect that your brain evolved to make you feel miserable at your perceived loss of status.
So if this hypothesis is true - and it is just a hypothesis (google "costly signalling theory" and go nuts). What advice would it suggest in terms of managing relations between scientific institutions and the public?
Well - I think it would suggest that you as Scientist should do better to control your own signalling behaviours driving you to seek recognition of your status and start thinking about what the public's own signalling behaviours imply they need and want - what will placate them?
And what they want - is the same thing you want. Status. So just give it to them. It's the EASIEST thing in the world. Rather than hitting them over the head with your technical, long winded "patient" explanations - that ring in their brains as nothing more as another status play by the know-it-all scientist... instead, praise their passion, tell them that you scientists are indeed working on every conceivable angle - really show that you are engaging with their suggestions - no matter how crack-potty they may actually be. And maybe at the end of your comment just throw in something like: "but of course we need to be really cautious, because of concerns x,y,z..." - so that your comment has a little educational value as well.
And if this means blowing a few million here or there on some dumb projects so the public feels like the things it cares about are being looked at - then it's probably worth the cost - insofar as we interpret that as a signalling act that conveys the idea that they do have status, they are part of the process... etc.. I'm sure that with practice - we could get the costs of these faux labs/experiments down to a minimum, while getting maximum signalling yield out of them.
But doing what your doing - self-deceptively going about on forums with your so called "patient explanations" as if you don't actually care about your status being ignored, when you clearly do, given how you erupted to accuse not just the public, but the whole institution of science of being guilty of crack-pottery - this behaviour is incredibly harmful when you view it from the point of view of the status signalling that is in play.
This is my advice to you OH PROFESSOR OF PHYSICS! Take it or leave it. :)