The confounding factor is that the layperson's suspicion that some academics are lying or involved in some conspiracy is not always wrong. Then there are the culture wars between various factions. Witness how computer scientists think of the social scientists in general. Not much love being exchanged there, they might as well be different species.
I think the only thing you can really do educationally is teach logic and thinking from first principals as well as heuristics for bullshit detection.
My technique is to pin down the person with a clear definition for a piece of their explanation. I then write this down. Eventually I find their ideas to be either consistent or inconsistent. Being consistent doesn't make them right but it sure does filter out most bullshit. It's like being a detective!
Unfortunately bullshit detection, first principals + basic logic only take you so far because for many real world things you require large amounts of domain knowledge. Teaching all that is impossible. You can however teach about what Neal Stephenson called icongraphies in his book Anathem. There are historical patterns, mental models that are domain specific but which can enable you to rapidly detect whether something fits into a framework or whether it's off the rails.
Here is a fair warning though. There is some interesting ideas about the split between 'American science' and 'Russian science'. That is something that shouldn't have happened but the communication breakdown led to several fields taking different paths. For example Geology supposed in America that Oil was generated from a biological source in the distant past. You might take that idea for granted. But in Russia it was thought seriously for a long time that Oil was generated from a non-biological source. I don't know the real answer myself but it is worth knowing that this does happen. I mean... one of them is almost certainly wrong.