By itself, it doesn’t really matter. As Holmes said, it wouldn’t make any difference at all to the life of the average person. However, it matters a great deal because it is positive proof of a much broader ignorance. And that will affect people.
To believe that the Sun orbits the Earth reveals that a person has no knowledge whatsoever of either the sizes of the Earth and the Sun or of basic physics: inertia, momentum, gravity etc. We’re not talking here about an inability to pass a high school physics exam. The belief requires utter and total ignorance. These people have to believe that the Earth is much larger than the sun, or else believe that the Sun-Earth system is held in place by some magical force unrelated to gravity. And that in turn means that these people must live in complete ignorance of what the sun actually is and what it does. It’s just not possible to have even a basic understanding of these facts and believe that the Sun orbits the Earth. And with no knowledge of the Earth-Sun system, these people don’t understand at all what seasons are. They don’t understand why seasons are reversed in the southern hemisphere, for example.
And this level of ignorance extends ever deeper, and eventually it does start to affect daily life. With no knowledge of the basic structure of the solar system, it becomes impossible to evaluate claims made about climate change, for example. There is simply no starting point by which any evaluation can be made. With no knowledge of seasons, it’s impossible to understand why you don’t want to travel to Rio for your Christmas vacation. And so on and so forth.
And this is the problem with poor science education. It’s not that people don’t know irrelevant facts about the solar system, or whether humans lived alongside dinosaurs. Those things aren’t important to anybody. The problem is that those beliefs are positive proof a deep-seated ignorance. The beliefs simply aren’t compatible with even a basic understanding elementary science. It’s not ignorance of the trivia that’s the issue. It’s that evidence of the trivia is proof of ignorance of the subject as a whole.
It’s that lack of a basic foundation in science that becomes dangerous. It leaves people with no ability evaluate the claims that are presented to them everyday. It’s the reason why people buy into quack remedies, pseudoscientific conspiracies and nutty cults. A basic knowledge of science is necessary to be able to judge whether a perpetual motion machine will work or whether Black people are closer to chimpanzees. And these people lack that knowledge because they lack any sort of scientific knowledge. Knowing whether the Earth orbits the sun won’t stop someone believing in perpetual motion machines or that Black people are closer to chimpanzees. But without that knowledge, you can be pretty damn sure that these people lack the knowledge that is required to assess a claim of a perpetual motion machines or a claim that Black people are closer to chimpanzees.
In short, it doesn’t matter in itself. But it’s incredibly important insofar as it is a very reliable symptom of a much more serious problem.