I played Altis Life at my friends house today and the cops were just super serious. They were all on team speak and if you weren't you'd get kicked, like what the hell?!
They're the equivalent of DnD nerds.
Maybe it has to do with the fact that ARMA is more of a simulator and not just another FPS
That sounds like a roleplay server. I would not be surprised if they kicked you.
It's a simulator after all. People really enjoy the realism and want to make the immersion perfect by roleplaying and by "taking it seriously". If they have a rule on that server that you need to be on teamspeak in order to play there then you should have done so. Most of these rules are there to ensure the best possible gameplay for the ones playing it. Simple as that.
Also there are lots of small, tightly knit communities within the Arma Realm. They are all really just about better immersion, and you have to imagine all of the stupid people who come on their servers and troll or ruin things.
I had a similar problem when trying to play AOE 2 online (via voobly--before the remastered edition came out on steam), where anyone I tried to play with demanded that I could be random team, random civ only, and kicked me if I decided I wanted to ensure I wouldn't be the Celts. Some people are just picky.
So a RP server in a military sim. Maybe you shouldn't have joined and played something else?