So what is it really? A social club? A church? A religion?

Church/religion. Flat-earthers believe in a very literal interpretation of the Bible which dictates that the earth is flat.

When I was doing my student teaching, one of the teachers in my department was a creationist, but he didn’t seem to have read Genesis 1 at all because when I asked him about the firmament in the heavens separating the waters above from the waters below, he had no idea what I was talking about. At least the flat-earthers know enough scripture to follow their dogma all the way to its absurd endpoint.

"Flat Earth"[0] is more like a cult[1]. One introduces a significant barrier to entry. New members learn the approved vocabulary/jargon that identifies "in group" and "out group" people. Outsiders tend to reject new members[2]. New members tend to stay due to the "sunken cost" fallacy. The high barrier to entry and cost of leaving (losing your community - because you will be shunned for doing so) prevents people from leaving or associating with people who have left.

Notes:

0 - https://rationalwiki.org/wiki/Flat_Earth

1 - https://rationalwiki.org/wiki/Crank_magnetism

2 - This is why religions such as Jehovah's Witnesses require members to proselytize (including going door-to-door) because outsiders are so adverse to the members that the other insiders remark things like "those outsiders are so depraved, that's why you can only be with 'true believers' like us".