This is a complete misconception in terms of Forgotten Realms lore. You could always play a drow male priest of Lolth in all editions of D&D. The problem is, most Lolthite societies would have you killed for it, since gender roles are very rigidly defined. However Lolth herself is a goddess of chaos, and who thrives on chaos, and if it serves her purpose, she might allow a drow priest to gain spells from her, provided the priest is in some way following her designs.
@Svalr: I didn't say there was a problem with wanting to play a non-evil drow. I was just pointing out that non-evil drow are extremely rare and that there is no problem with the race being almost entirely evil in this fantasy world. I say that because this is not the first time that I have heard crap about Wizards softening the drow to be less evil because, ALLEGEDLY, they don't want the dark skinned race to be the bad guys. I don't know if that is true but I certainly hope it is not. I really grow tired of attempts to make fantasy worlds reflect the modern real world.
Not as rare as you seem to think. There's been good drow for a long time, just Drizzt managed to steal the spotlight. (I love Drizzt, honestly, but sometimes I wonder if his novels have been detrimental to the rest of the Forgotten Realms.)
Lolth is not the only drow deity. In fact, there is another deity in the list for BG3, Eilistraee, who is a Chaotic Good drow deity. She's had followers forever (because if she didn't have any, well, that's how gods die). So good or neutral drow are more common than you'd think. Additionally there are some drow cities where Lolth is not the premier deity or where the harsh matriarchal hierarchy does not exist (see Ched Nassad).
As for making them less evil because they're a dark skinned race, what nonsense are you talking about? In some ways, this is just making the drow more realistic - no one group of people is a monolith. Drow have had all sorts of "shades" to them from the get go - not just evil "shades".