Of course, if the nation which inhabit surfacer drows, is used to them, perhaps certain drows have complated acts of valour, heroism, defended the nation against outside threaths, the common view might have changed and become slightly more tolerant of them. But still. They wouldn't be your friend. They wouldn't be your drinking buddy. Especially you wouldn't invite them over, to play with your kids. The horrible, evil, acts drow have commmited are also things, that most of the common people would know about. From tales, stories, they would have heard about the acts of horror, this dark race had committed.
Example:
If you heard that a killer of children was in town, would you pat him on the back, and introduce your children to him? No? You would rip him apart, and let the vultures have a feast?
But these are just my thoughts, and of course, this is RP and I hope nobody take this rant as an insult if they are playing drow, it is not ment as such. I am not saying you should play your own chatacter any differently, or you should start treating drow like they had just stolen your lunch money, and sank your head to the toilet. Rp is individual, every character is different, every city is different. I am just saying how drows are viewed in FR, by the majority of surface races, and underdark races as well.
EDIT: This was ment for the perspective of a common man (alignment neutral/good)... Criminals, and other evil aligned people would be complatelly different story. They might consider thge drow as powerful allies, due to their rebutation. Still, even criminals and whatnot evil aligned people, they would not trust the drow, but they might work with them for their own benefits.