Except that you don’t believe the two are equivalent as conventions or just coordinate systems - you think one view is correct and real and the other is incorrect and only exists in people’s minds, no?
So the Earth going around the Sun, does that only exist in people’s minds?
Again,
"... it is the main tenet of the Einstein theory that any two ways of looking at the world which are related to each other by a coordinate transformation are entirely equivalent from a physical point of view.... "
Hoyle, Fred. Nicolaus Copernicus. London: Heinemann Educational Books Ltd., 1973.
"So the Earth going around the Sun, does that only exist in peoples minds?"
Again,
"What I want to bring into the open is the fact that we are using philosophical criteria in choosing our models. A lot of cosmology tries to hide that.
Ellis, George, in Scientific American, Thinking Globally, Acting Universally, October 1995