That educated people believed that the Earth was flat is largely a myth. Not only people knew the Earth was round since antiquity, but they also had a good idea about its diameter.
Heliocentrism was a bit more debated but for good reasons. Early heliocentric models were actually worse than contemporary geocentric models to calculate the motion of planets.
All that to say that "everyone else is wrong" doesn't happen often in practice, at least not among educated people. And when that happens, either the evidence is solid and it is generally well accepted or it is not, and there is no reason for others to accept it. The burden or proof is for the one who makes the claim.
To go back to heliocentrism, the reason it is the prevailing theory right now is because the model has been refined and now, it matches observation better than older models based en epicycles. It is not because of some philosophical reason about our place in the universe.
