On the contrary, SR and GR have more in common with flat earth belief.
In fact, Christians never believed in a flat earth. It was a part of Hindu religious mythology, not Christian. Hindus believed that the earth was flat and was held up by elephants standing on the back of a turtle.
Various cultures have had conceptions of a flat earth, including ancient Babylon, Ancient Egypt, pre-Classical Greece and pre-17th century China. This view contrasts with the realization first recorded around the 4th century BC by natural philosophers of Classical Greece that the earth is spherical.
The belief that medieval Christianity believed in a flat earth is simply false.
St Augustine, writing in The City of God makes it perfectly clear that he recognised there were Antipodes (i.e. a circular orb of the earth with poles at each end).
So, to all the dummies out there who thought otherwise, no, it is nothing to do with a flat earth.