As much as this is certainly the case (people using models wrong is one of my personal pet peeves), there are at least as many people who take equal and opposite extreme moral and political stances on account of the model being inaccurate.
Anyone who actually understand EMH just takes it for what it is.
> beliefs without scientific support
Any political or moral belief is a belief without scientific support. Those are simply not things within the domain of science. Anyone who says otherwise is just trying to bamboozle you into some weird ideology.
But this wouldn't affect thoses stances (in either direction). An EMH advocate can just (rightly) say, "Markets are efficient up to the limits of computation speed." Those same limits apply to anyone else's attempt to correct the market, so it doesn't validate view based on its negation either.
In my view it is a good thing to prove the model wrong, because so many people take extreme moral and political stances on account of the model being accurate.
At the very least, displaying counter-examples is a way to show those stances for what they are, exposing them as beliefs without scientific support.