Sorry, bit of a long post, but ...'Earth is flat', definitely.
The evidence that Jesus turned water into wine is John's Gospel, plus some non-gospel comments about him being a magician. On the other hand, the evidence that he didn't is that it would require Jesus to have a complete control of matter down to the sub-atomic level. Which is admittedly a bit of a mind-bending idea.
But, if you're a Trinitarian Christian, there is no theological problem with Jesus having a complete control of matter (down to the sub-atomic level), owing to the entire 'He's God' proposition. Basically, it boils down to 'If we believe Jesus could do the things God did, do we then decide to believe John's account or not? He seems to be the only witness to this wine thing.'
'The Earth is flat', on the other hand, requires you to actively and continually reject visual, documentary and experiential evidence that the Earth is very much not flat.
What I've noticed about our friends is that they are unable to provide evidence when asked and they avoid defining their terms. They also reject the evidence that transwomen, far from being identical to women, behave as a subset of the sex-class 'men'.
To maintain their beliefs, they have to continually 'reject the evidence of their eyes and ears.'
It's much more 'the Earth is flat', and very different from early Christianity. There, we have letters basically saying 'you can talk to these people, who met Jesus.' Or, 'well, one of the post death appearances was seen by me, and another by a couple of hundred people'. Likewise, the response to 'people don't rise from the dead' was basically, 'Yes, it is weird. We know'.
That's a bunch of people who were accepting the evidence of their eyes and ears, even if that evidence went against the common sense of the day.
There's a big difference between 'this is very weird, now here is our evidence for this weirdness,' versus 'What do you mean by calling this weird, shut up you evil person! We curse you and banish you from our sight!'
The first is a religion. The second's a - well, I'd use the 'c' word. Or a religion that's gone toxic.