NPR has one of those “shocking” headlines: “1 In 4 Americans Thinks The Sun Goes Around The Earth, Survey Says.” This amuses me, not from any sympathy for geocentrism, but from a certain admiration for people who stubbornly refuse to believe or show any particular interest in the various things their self-appointed betters insist they ought to. This drives “the smart people” to distraction, but the reality is no normal person ever has to calculate planetary orbits, nor is he likely to encounter even the slightest practical application of cosmology to his everyday life. That even holds true for the overwhelming majority of those who actually work in the sciences or engineering.
(And if you are calculating planetary orbits, my impression is that it’s easiest to calculate orbits around the centre of mass of the entire system, not the largest body. In the case of the solar system, that’s close to the sun, though not necessarily always inside of it. Maybe pedants should start sneering at people who think the earth orbits the sun. They both orbit the barycentre…)
Science is probably far more retarded by actual scientists afraid to consider certain ideas for fear of scorn or loss of funding, than by non-scientists with eccentric—even wrong—ideas about esoteric topics.