I dunno what else I can say here that hasn't been said in ten thousand other posts. For whatever my own two cents are worth, "how to play an antagonist(ic) PC" is something that varies from game to game and is a thing that the people running the game should manage from the outset, if they want antagonist(ic) PCs at all.
If someone's playing their character in a way that's antagonistic to the point of disrupting how a faction operates IC, or that leaders of the faction are more willing to change how they operate than risk another evening spent butting heads in a scene with Antagonistic PC, then IMO it becomes something staff should address and decide whether or not that's what they're okay with in their game culture (it might be a game culture where the expected answer for someone being too frequently and too frustratingly insubordinate is just to blast them with a shotgun, who knows).
For antagonists, which @faraday rightly pointed out are different than just antagonistic PCs, staff should be even more actively involved in putting forward what they expect from all sides of the conflict.
I'm going to make up a WoD example. It's not going to be a very good one because whatever I'm on my lunch break.
In the one Vampire splat, you've got Camarilla and Sabbat and they're against one another as one would expect. Staff's job there is to be clear with everyone about the rules of engagement and what can be done where and when. Otherwise PVP happens and someone yells "no fair" -- which will happen anyway but at least if staff is proactive in describing the kind of PVP culture they expect or the kind of PVP rules they mandate, hopefully people will know what they're in for if they play.
In the other Vampire splat, you've got Camarilla and Sabbat and the staff there is hoping to do a metaplot story about werewolves circling the wagons around the both of them. Staff's job there is to make it clear that the antagonists are the NPC werewolves, even if the Cam and Sabbat can be antagonistic toward one another in how they work together (or fail to work together) to keep their city from being gobbled up by The Howling II. Staff will also need to be proactive in keeping that wolfy metaplot active and engaging, because otherwise, people will get bored and default to "well, I'm a Sabbat, and that Camarilla just insulted me, so it's on."
Anyway, my point is, whatever the way to play either a jerk or a bad guy is on any given game, it has to be something that the people at the top of the pyramid have given thought, and made those thoughts clear toward the player. Cuz otherwise people will just do whatever they think fits and it's never one size fits all.