I'll start by conceding, so as to avoid being a crank myself, that I have no special expertise on the topic, but will just offer some informal thoughts.
The question, as I understand it, is whether, if a person, especially an outsider to an academic field, demonstrates lack of technical understanding in a subject they discuss, that discredits their public pronouncements more generally. My position is that while there is some negative information in technical errors, it is easy to overdo negative inferences, and there are costs of going too far.
First, the quality of comments made by most people is quite varied. So if our policy is to keep close track of mistakes in informal venues like Twitter and consistently heavily discount subsequent comments of those who have made mistakes, we would be dismissing many people, including our colleagues.
I’ve noticed that philosophers I admire typically said both brilliant things and very wrong-headed things. In general, making mistakes is an important part of the knowledge generation process, and it often takes a lot of mistakes to produce something of value. A willingness to tolerate mistakes is important, and, with e.g. great thinkers, we select, out of many things they say, the best, and discard much else. I don't think it is accurate about human beings that they just produce high quality or low quality thoughts; in general, people produce a mixture. Yes, some people are better on average than others, but making informal inferences about this can be hard.
I am not saying that we shouldn't keep track of people's intellectual reputation, but just that we should have some humility in doing so.
Second, I think that it can create a bad culture for insiders to be quick to dismiss outsiders who don't conform to inside conventions and consensus. To some extent, this involves a certain kind of gatekeeping, as if we are the guardians of our intellectual domains. But we actually want people to engage more broadly in the topics that we study, and we don't want to discourage participation by policing outsiders and holding everyone to our academic standards.
Gatekeeping makes a bad impression. We don't want to rely too much on our authority as experts. If, when we spot a mistake, we explain in accessible terms the reason it is mistaken, rather than accusing the person of an esoteric technical error, or saying that they are a proven crank, then onlookers will be better able to assess our claims. But that looks much more like judging claims on their merits rather than claiming that a person has proven themselves unreliable.
In many cases, there is little harm in errors made by outsiders to a discipline. However, some people have large followings who they can mislead, which can have consequences. But even then the best course usually is to explain why what the person is saying is mistaken rather than saying "take it on my authority, this is the sort of person you shouldn't listen to."