It all depends on how serious you take it. Having a Horde sticker on your car because that's your faction and you like it is fine. Yelling "for the Horde" at a stranger in a Thrall tee shirt is cool. Being verbally abusive to a stranger in real life for playing Alliance is embarrassing on a lot of levels.
I've never known anyone personally who took factions seriously outside the game, but anyone who has gone to Blizzcon knows those people do exist. One of the many times I was waiting in line one year, the guy in front of me turned around, grabbed my arm, and angrily demanded to know what faction I played (my answer was apparently satisfactory and I escaped disturbed but unscathed). But even then I'd like to just hope the scarier nerds are just caught up in the excitement and not really "like that."