In general it would be great if people were more knowledgeable, our conversations were more enlightened etc. etc. - no-one will disagree with that.
But I think there is a dangerous elitist fallacy lurking here somewhere. The validity of your opinion about subject X isn't always strongly dependent on your knowledge of subject X. Let me make up a simple example. We have a choice between getting a red rock or a green rock. Some of us have a utility function that prefers red to green. Others have a utility function that prefers green to red. But a further group derives utility from complex molecular properties of rocks. Some of them have put forward elaborate arguments for why the red rock would satisfy that utility function better. Others have put forward elaborate arguments for the green rock. By contrast, the red-utility people and the green-utility people haven't put forward any elaborate arguments. In fact they haven't studied the issue much at all as it's extremely straightforward to them. This irritates the teams with the elaborate arguments and they feel the first two groups aren't really entitled to an opinion on which rock to pick. Yet, it seems to me that they are perfectly rational in how they approach the issue and have as much right to an opinion as the sophisticates.
And I don't think this is a particularly contrived example - I see a similar thing in the debate on whether my European home country should use the euro as a currency or not. Some people oppose European integration on principle (they're in favor of local government or they're nationalists or whatever you want to call it) while others support integration on principle (they're one-worlders or internationalists or whatever you want to call it). But then there are elaborate economic arguments on whether using the euro is of economic benefit to the country. The sophisticates really do tend to think that the people who haven't immersed themselves in this economic debate aren't entitled to an opinion on whether the euro should be used. I think that's wrong.
I don't see how it makes sense to reference nationalism or internationalism as terminal values. They are instrumental values, and their effects on a population's happiness/fun/quality of life should be studied and discussed. There are other valid perspectives besides economics for evaluating the issue, such as the sense of community a system promotes, but when people state simply that they value a certain system as a terminal value, their only contribution is the anecdotal data about their own preference.
I think the analogy breaks down in that the utility ...
A currently existing social norm basically says that everyone has the right to an opinion on anything, no matter how little they happen to know about the subject.
But what if we had a social norm saying that by default, people do not have the right to an opinion on anything? To earn such a right, they ought to have familiarized themselves on the topic. The familiarization wouldn't necessarily have to be anything very deep, but on the topic of e.g. controversial political issues, they'd have to have read at least a few books' worth of material discussing the question (preferrably material from both sides of the political fence). In scientific questions where one needed more advanced knowledge, you ought to at least have studied the field somewhat. Extensive personal experience on a subject would also be a way to become qualified, even if you hadn't studied the issue academically.
The purpose of this would be to enforce epistemic hygiene. Conversations on things such as public policy are frequently overwhelmed by loud declarations of opinion from people who, quite honestly, don't know anything on the subject they have a strong opinion on. If we had in place a social norm demanding an adequate amount of background knowledge on the topic before anyone voiced an opinion they expected to be taken seriously, the signal/noise ratio might be somewhat improved. This kind of a social norm does seem to already be somewhat in place in many scientific communities, but it'd do good to spread it to the general public.
At the same time, there are several caveats. As I am myself a strong advocate on freedom of speech, I find it important to note that this must remain a *social* norm, not a government-advocated one or anything that is in any way codified into law. Also, the standards must not be set *too* high - even amateurs should be able to engage in the conversation, provided that they know at least the basics. Likewise, one must be careful that the principle isn't abused, with "you don't have a right to have an opinion on this" being a generic argument used to dismiss any opposing claims.