I personally don't hate drow and of all those I play with they don't specifically hate drow. Sometimes they seem a little overused, but that's not really any reason to hate them.
To me, most of the hatred towards drow stems from the fact people like to make Drizzt rip-offs and some people just hate playing evil characters. Playing an all-drow campaign could be really cool, especially within in drow culture.
Drow, in my perspective, are all the same evil. Not saying half of them are good or anything, you just get different shades of evil inside a drow city, and alignment could become more of a roleplaying issue since everyone is evil - but not all the same villanous evil.
I'd say running a drow campaign would take more roleplaying than some people appreciate in a standard D&D campaign, because the differences aren't so black and white. Culture, perspectives, and hierarchy would probably be my focuses in a drow campaign. You can also have the drow move as a co-ordinated group (eg. hunting a band of mindflayers, or a raiding party to a nearby village/city whether underground or not). Conspiracies and plots would abound, as might be expected. Playing a drow campaign, for me is like playing a campaign in a royal court: everyone has the same public face but is working behind the scenes to further their own ends.
No problems, and really cool.
Viashimo