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).
Your comment piqued my curiosity so I did some reading up on the Fandom Forgotten Realms wiki. According to the page for Drow on there, it does state that approximately 15% of drow were not evil but of that 15%, most were neutral, not good. It does mention Ellistraee being worshipped by the ones that were actually good but "the morally neutral drow's worship was split among Ghaunadaur, Lolth, Selvetarm, and Vhaeraun." I would be interested to learn what other notable good drow you are aware of besides the ones I mentioned earlier because the entry doesn't really mention any individuals in that category.
I also looked up Ched Nesad on there: https://forgottenrealms.fandom.com/wiki/Ched_Nasad
since I knew that is where Rai-guy that I mentioned earlier is from.
According to that entry, and it's footnoted pretty well, Lloth is or (I guess was) indeed the primary deity there and the city was actually founded with Lloth's blessing by exiles from House Nasadra of Menzoberranzan. The article mentions no other deities besides Lloth and additionally states that the prevailing alignment of the city was NE and CE. It also mentions that while it was a matriarchal society, it wasn't as strict a matriarchy as Menzoberranzan so it concurs with you on that.
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".
So in my comments above I capitalized the word 'allegedly' precisely because that is just what I have been hearing on forums pertaining to this game. I haven't been involved in following lore changes from Wizards in quite some time so I don't have first hand knowledge of how the drow have evolved from strictly evil NPCs to what they are portrayed as today. I've seen it mentioned several times, had it just been a single instance I would have discounted the validity of it but it seems to be at least a somewhat widely held belief.
Anyway, I appreciate the discussion as it is interesting. Last night I didn't even play the game, just sat on here and discussed it which I also enjoy so thanks for indulging me.