Ohhh, Special-Snowflake-Drow time? Tighten your seatbelts, put on your hardhats, secure your Evil-DM-is-EVIL whips to your main hand and the GM-Bible to your left, this is going to be a tough ride. Because, if they want to be so special, the one in a million good Drow, they got to pay for it. With good roleplay!
##Your Alignment Is Not On Your Face
Or freshbaked Drow-outcast washes up in socalled civilized lands. Lands, that claim to be Lawful Good. And of course, everybody in these lands knows what a hero looks like: they are paladins and shining knights, mysterious gentlemen and the like, but most certainly not the mose evil thing that one can think about: Drow. If one shows up, that must be a bad omen, a spy for the Underdark, a scout for an invasion. The only sensible things to do for the population are:
- Hide your wealth, your daugthers, maybe even yourself! The drow can't steal and murder what they don't know about or find.
- Watch it carefully, for any misdeed it does! And then drag the evil creature in front of a judge and demand the full power of the law, piling all the tiny deeds upon him together with the misfortune that happened. And a Drow at the gallows is a spectacle that will sooth the masses for a little time.
- Mob it, if you can outnumber it 10 to 1 and under the leadership of a high cleric or paladin, bestowed with the task to slay these evils. Because, the mob has the right of pitchforks and torches.
Ok, that was very graphic but what I want to say here is: If they are laty and just are a 'special snowflake drow' by the book, throw him all the stereotypical hatred of the drow you can, because the population doesn't know it better and can't know he is this. Warn your player about this. Tell them that you won't pull back, because Drow are considered Always Chaothic EvilTV Tropes by the general population, and if they are fine with that.
##Fear The Unknown
On the other hand, we might not even need to unleash the hatred of the populance. They might not even know Drow exist in the first place, making the PC the first they encounter! But, what makes a noble elf's skin as black as charcoal? What wretched magic must be at work there! Either this individual must be in league with the dark forces or a really unlucky bastard. But better play it safe.
Unlike in the previous route, the general populance should stay at points 1 and 2: Warily eye the drow for evilness and signs of corruption, maybe demand holy cleaning rites to make sure they are not evil. Repeatedly. And swearing upon the good gods that he has never done and will never do an evil deed.
This is pretty much the Fantastic RacismTV Tropes light. This is the option if you don't want to be the totally evil GM that unpacks the full force at any circumstance. You might want a mix of the two approaches at times. But there is more in the trickbox!
##Everybody fights, noone quits!
Ohhh, you are a Drow outcast, someone the hightly structurized society of the Underdark does not want? You know that the Drow houses never leave loose ends, right? They will make sure to try to tie up this lost thread: either by returning the sheep to the fold or by ending it. Or even more sinister: They might not even go after the traitor themselves, but after their friends, those that they learn to like, those that are left in their path as people having fond memories of them.
In time, the poor Drow will learn that the village they saved from bandits was sacked by his breathen and brought to the citadel as slaves. The wizard they returned the ancient spellbook to was forced to use it to summon an ancient old horror. And to stop this, the hero themseves has to return to the citadel to turn themseves over to the high priestesses of Lloth...
This would focus your whole campaign around the Drow. Make him a pivotal point... and pervert some of the deeds of his group. Turn them into villains against their will. And maybe, maybe in the end they embrace this lot. Turning to evil fully.