Iv'e been tempted to watch that doc for awhile now but its hard to get away from binge watching the office lol. As a "christian" (and I use that term loosely) I dont believe that the earth is flat, nor do I believe that it is perfectly spherical, due to shifting tectonic plates, seismic activity, gravitational pull, etc. etc. could all warp and shape a planet thats in constant motion.
I'm not sure what there is to gain from spreading flat-earth theory or vice-versa other than to spark attention/enlightenment and cause people to start digging. Thats what happened to me after I saw Zeitgeist for the first time. Growing up christian I was pretty much spoon-fed christian/catholic dogma, but after Zeitgeist I realized I needed to dig deeper into my faith and find out if what I was raised to believe was actually true, and I got the answers I needed. I dont think flat-earth or round-earth is really that big a deal, what is a big deal is exactly what you pointed out, the insulting, name calling, and downright asshole reactions from the opposition.
There once was a man who said "love your enemies" and "do good to those who hate you", and thats the man I try and emulate, and I could only recommend that to anyone being bullied or persecuted for what they believe in.