This is beyond foolish, and untrue, and if it were true, it is a relatively new phenomenon.
People do not believe the opposite of what experts tell them unless encouraged to do so, and given a set of plausible reasons.
While sometimes this has merit (because experts are not always right), it is almost always done by people who having something to gain from a public discordance with expert opinion.
In addition, "experts" have been made much less visible in our society than they once were, largely due to the democritization of communication technology but also the concomittant rise of self-promoters. A lot of the reactions to "experts" are actually just reactions to noise.
Finally, the single most important issue with public/expert interactions IMO is the media-driven lack of tolerance for nuance on the part of the public. People are much less willing to accept actual expert answers, which tend to be of the form "well, it could be X, but it could also be Y, we probably won't know until we do Z". Consequently, a secondary stream of not-actual experts emerges, who provide the handholding answers like "It's X", and this is then used to disparage actual expert opinion when it turns out to be Y.
There are fields where "expertise" is hard to establish and of limited utility, and the expression of opinion there is primarily a statement of ideology and desire. I think that severe skepticism is warranted there, even more than the general skepticism one should apply. But FFS, it is what "experts" know and do that has bought us so much power, agency and comfort in the world, and the idea that believing the opposite of them is a good heuristic is just nuts.