I've given up debating with flatties. They are in denial about science. It seems to be part of a general suspicion about any authorities and certain politicians even encourage such behaviour. 

The 'conspiracy' would have to go way back beyond Galileo as the ancient Greeks had measured the Earth and knew it had to be a sphere even if they didn't understand gravity.

Science is not about what you believe and you have be prepared to be proven wrong.

BTW I work in the space industry, so I hope it's real :)