If their dialogue lines are the same for Drow and Human, I wouldn't expect any special reception for drows / giths in the city. Because otherwise it would be a very poor writing on Larian's part.
As someone who primarily plays Drow/Githyanki and Tiefling characters, the Drow have the most racial reactions coming from NPCs, followed by Githyanki and then the Tieflings. And not only that, but even Lolth and Seldarine Drow get different responses too to such comments.
So I don't think there's any reason to worry about, as even now in Early Access the Drow is treated as a rare and fear instilling occurrence. And there are scenarios where the Drow exclusively gets a free pass, such as the Goblin camp, where the encounters are pretty different compared to other races.
So nothing really points towards the Drow being treated the same as the other the races.
