It's not the most violent soccer club by far. I saw a ranking and St. Pauli was on place 15, the first one being Frankfurt and the second Dynamo Dresden (what is a known right wing club).

The club does a lot of social activism and most fans in Hamburg are pretty normal social democrats. You are not wrong that there is an overlap of St. Pauli fans and the left scene in Hamburg. It's not a stretch that a militant person from Hamburg would also be a fan of this club. That's about it and how it probably ended up on that list.

Also the squatted building you are talking about is now owned by the city that basically allows its current use.