I for one think it's handled quite well at the moment:
- those two guarding La'Zel basically shit themselves upon encountering an "underelf"
- upon entering druid grove Zevlor specifically mentions they were taught to fear the drow, but that you've earned your place here and he's gonna update everyone on it, so that explains why they're mostly accepting. Still someone definitely mentions being
surprised about you not walking around in disguise
- Burning inn - well they have a certain emergency going on so it kinda makes sense to accept help wherever it might come from and you're not accompanied by goblins so...
- as for Goblins you're a drow and True Soul so I don't think that even warrants further debate - worth mentioning Drow disguise works here as well (either on PC or any of the companions)
- Zhentarim - as evidenced by Roah they're currently working with goblins and the drow sooo
- Halsin actually expresses some sort of disdain and you can even confront him on it
So to drow a line (couldn't resist) I expect some problems later on, maybe even an obligatory disguise for some places but so far in-game reactions to PC being drow make sense.
I think it all makes sense except for burning inn. I mean, their dude was captured by drow. And they have no reaction at all to a drow showing up... And even in normal circumstances they should probably turn hostile on drow. I don't think the reputation of the drow from the flaming fist has changed in the last 100 years.
At the very least you should have to do a very difficult persuasion check to convince them you're actually drizzt or something.