Popular false beliefs always seem harmless until they suddenly aren't. The principle of explosion means that one false belief can justify literally any course of action, and by the time people start on a harmful course it's too late.
For the principle of explosion to work you have to actually confirm that a belief is false, or at least calculate a justifiable probability that it is false. You can't just assume that it is false and extrapolate from there.
The point is you can't assume it doesn't matter because it seems harmless-if-false. The grandparent asked "why do you care [whether the things Musk is saying are true]?", but the answer is that you have to care about anything that's likely to influence a large number of people.
