If it's red, it's dead
The simplest way to resolve this dilemma, some would argue, would be to kill every enemy in sight. It certainly would be in character. It also conveniently explains griefing lower-level players... ruthless members of the <insert faction here> slaying would-be future heroes holds much strategic advantage. On PvP or RP-PvP servers, corpse-camping and ganking are completely fair game, making the option easy and repercussion-free. The opposing faction can't understand you, anyway, so why bother, right? Well, technically, sure. The only real problem with such an easy solution is that it's deathly boring. It's dull. Even outside of role-playing, I've always found ganking to be completely uncreative and uninspired. In fact, if there's any character that ganking will portray you as to the opposing faction, it's as a jerk. Not much depth there.
There are far more sophisticated ways to play your character in front of your (often quite literally) toughest audience. One of them is the Battlegrounds, where there are specific goals to achieve and factions to fight for. In Warsong Gulch, one allies with either the environmentalist Silverwing Sentinels or the industrial (as I'd like to see it) Warsong Outriders; in Arathi Basin, one can be under the employ of the Defilers (with a name like that, there's just no getting around bas press, I'm afraid) or a volunteer for the League of Arathor; in the epic Alterac Valley, one can be a grizzled soldier for the lore-entrenched Drek'thar or fight proudly among Vanndar Stormpike's noble guard. Battlegrounds help you get into character, provided there's enough lore for you to build upon. I lamented on the lack of a backstory for the Eye of the Storm, but I'm sure battling in an alien environment has its applications. It's pretty good stage design, at the very least.
Participating in world PvP objectives such as capturing the towers in the Bone Wastes or even -- gasp -- sandlol in Silithus can get you in the right frame of mind for role-playing your faction from a PvP standpoint. This still doesn't solve our primary dilemma, however. This is all still just conditioning. Method acting, if you will. What follows is establishing your character with your audience or fellow role-players. Custom emotes are out of the question, as all players of the opposing faction will see is that you are "making some strange gestures". Blizzard prudently curtailed that avenue for cross-faction communication from the get-go. One small workaround is to use a Priest's Mind Control to enable viewing custom emotes. It's a temporary solution, but can be used to send the right message at the right time.
What are usable on a more regular, reliable basis, however, are normal emotes that are effectively one's secondary vocabulary to communicate with the enemy (the primary being the business end of your weapon or spell). A typical emote that one will see during PvP is the overused and uncouth /spit and condescending /laugh or /rofl. While those emotes get the point across, they give your character the emotional breadth of an asparagus. A little creativity is in order. Against formidable opponents, don't be ashamed to use /amaze to let your enemies know how you marvel at their skill. As with the highest order of combatants, a /salute also works to establish (hopefully mutual) respect among your enemies.
Some emotes work well together, such as /crack and /chicken. You can string emotes to more or less act out your part, albeit to the slight detriment of your PvP. Now that Battlegrounds are cross-server, you will be surrounded by non-RP players, as well, whereby your emote macros will largely be viewed as annoying. But used sparingly and creatively, emotes can flesh out your character a little more for the enemy. A little respect goes a long way, and the aforementioned /salute, given that it isn't construed as sarcasm, sets the stage for battle between true warriors.
Titles and reputation
Another means of fleshing out your character is by displaying the now-obsolete PvP Ranks. Aside from being a mark of personal achievement, it establishes one aspect of your character -- that you are part of your faction's great army. Newer characters can obtain Arena titles and the Battleground reputations titles. While sporting Grand Marshal or High Warlord no longer holds as much gravity as it did prior to The Burning Crusade, many (but most assuredly not all) of the people who obtained those titles were formidable opponents on the field. It also clearly establishes that those characters' focus -- at least once upon a time -- is or was PvP. Nowadays, it is the Gladiators who elicit a measure of respect and trepidation from opponents. Of course, there are a few who paid their way to their titles, so combat skills are always suspect until you actually engage in combat.
The best way to role-play through PvP, I think, is to simply be good at it. With enough victories on the field of battle, one garners a minor reputation. This was easier to do before cross-server Battlegrounds were implemented. During another time, another era, with enough immersion in the Battlegrounds, many players became familiar, even feared or respected. A long time ago on the first server I played in, one of my private, personal goals was to be recognized as a fairly decent PvP player. Thus I set about my plan which was to constantly face off against the highest-ranked player of the opposing team in a Battleground. I considered it a personal test of my skill while at the same time a cleverly disguised PR campaign. The highest-ranked players in a pre-made -- they only played in pre-mades -- were usually the leaders and had influential voices. Being a thorn on these players' sides would have a long-term effect -- first of annoyance, later of respect.
The server I played on back then had an Alliance-to-Horde ratio of about 2:1, and we often got rolled in Battlegrounds. Time and time again, I would be in a PUG faced off against the Grand Marshal team (the pre-made run by the current candidate for Grand Marshal) and we would be mercilessly crushed in minutes. Most Horde players then would simply /afk and queue for a different Battleground (such occurrences led to the creation of the Deserter debuff) but I would always stay and seek out their leader, a Night Elf Priest who was weeks removed from becoming a GM. On one thread in the Realm forums, a player asked who were the notable newcomers in PvP and this Priest, who was vocal on the forums, responded with my name at the top of the list. Being "annoying", as he liked to call it, had paid off.
Because it was a Normal server, it was common practice to create toons of the other faction and inspect opponents. As I played more and more PvP, I received tells from low-level toons reacting with surprise about my gear (I had somewhat noobish choices for a Level 60 back then) or complementing my play in recent games. These were alts of my enemies who had come to chat. The Grand Marshal Priest, in fact, who was a GM of a guild, later made a toon Horde side and joined my Guild, offering insights on both PvP and PvE. Cavorting with the enemy? Perhaps. But we had played our roles well. We met on the field of battle and found, as I would like to think, mutual respect.
Establishing a reputation is a great role-playing tool. But this kind of familiarity, or even rivalries, with opponents probably no longer happens with cross-faction Battlegrounds. There are simply too many players. The influx of questers also dilute your audience further. Furthermore, many good PvP players also concentrate on Arenas, making repeated head-to-head encounters exceedingly sparse. So how does one establish a rapport with the enemy if fighting alone won't cut it? Well, you can cheat.
Spread tales of your exploits and use means outside of the game to communicate it. Make a PvP video if you'd like. Start up a blog. Make a webcomic. Establish a presence on your Realm's forums. Sure, they're somewhat self-serving and definitely self-promotional, but they're excellent ways of putting some meat into your character for the people who will never get to see it from your faction's side. Paint the picture you'd like your opponents to see. It isn't too different from how Heroes' Takezo Kensei had a greatly exaggerated reputation where the truth was slightly different from reality. But that's the essence of acting, isn't it? It's make-believe. It's just like how movies nowadays are promoted through the MySpace pages of the fictional characters in the film. Understand that I advocate promotion, not deception; tall tales used as a tool to flesh out your character for opponents in an RP setting.
In my opinion, the purest form of role-playing one's faction is PvP. One must fight, not simply for personal gain, but to further the goals of one's faction. Simply by fighting, you are role-playing. You embody the role of a champion of the Horde or the Alliance. When you enter the Battlegrounds, you play the role of a hero. Not all members of the Horde or Alliance are soldiers. Faction NPCs are bit players, albeit cardboard characters, in the giant cast of WoW. Remember that poignant scene in Peter Jackson's Return of the King, where Faramir is bid a somber farewell as he and his troops attempt to retake Osgiliath? Well, you're the Faramir in this story and the NPCs the people of Gondor. With a less funereal tone, of course, and the happy benefit of a Spirit Guide to bring you back each time you fall in battle.
Faction loyalty -- and conversely, hatred for the opposing faction -- is a character motivation that needs little fleshing out. The entire game is rife with faction conflict. It is easy to pick up and play out. At the very least, use these motivational tools to put more substance into your PvP, if not the other way around. After all, if PvP is anything, it's a whole lot of improv. Happy hunting!