Hmmm ...
It would be genuinely interesting if a true Spider Deity, who actually WAS shy, peaceful, and gentle (but with a nasty bite!) woed the drow away from Lolth, to attempt to create a drow society vaguely (or even partially) similar to the humorous one I described.
Because if this started to happen, all chaos would break out.
Lolth would most definitely send her people after these renegades, but said renegades would be prepared, because the Spider Deity would have anticipated Lolth's behavior (in some ways, she is pathetically predictable.)
But now, word comes to the surface of a drow civil war. And, as with all rumors, facts get distorted, changed, and greatly exaggerated, an avalanche of misinformation in the making.
So the elves take interest and send spies to find out what is happening. Sages attempt to find out. Adventurers go for a look. Such notables as Volo get into the act (and they, of course, deliberately exaggerate, lie, or fabricate to create a 'good story' that sells, which may or may not stir up a panic.)
By now, the surface world has reason to fear it may be pulled into the war, which has now broken into many factions, as the clergy of Ghaundaur and Kiransalee are taking advantage of the confusion to try and take over Below, and Vhaerun is trying to take over Above.
So the surface world sends emissaries to the drow, in places like Skullport, to make alliances or 'deals' with the drow, to insure their own safety or to at least somehow correctly ascertain the situation.
Likewise, the other Underdark Races are now destablized, and they get into the act. The illithid are pulled into the war. This affects their slaves, who try to revolt, with help from surface humanoid nations. The githyanki, long-time foes of the illithid, realize they have a chance to strike at them. The githzerai, enemies of the githyanki, seeing them preoccupied, realize they have a chance to strike at them.
The beginning of war in the Astral Plane leads to more rumors, wild exaggerations, half truths, and panic. Now, the surface nations of Faerun have to deal with this problem as well, since the Astral Races could strike at them. (And indeed, the Shadowmasters, sensing their chance in the confusion, intend a massive strike at the Lord's Alliance.)
Then accusations start. Thay has allied with the drow! Dambrath has one hundred thousand drow ready to march on Halruaa. Aglarond is secretly helping the Spider Queen (not Lolth) drow. This whole thing was rigged by the Chosen. The Church of Xvim and Fzoul Chembral secretly started the war. Somehow, Manshoon (one of him, anyways) took over a drow city, and is preparing retribution against Zhentil Keep. The Shade and githyanki have allied! A Faction in Sigil is ready to declare war on Cormyr. The Scro of Realmspace are preparing to attack the illithid. The aboleth have allied with the sahuagin to take over the coastal Underdark. Halaster the Mad Mage and the Skulls started this. A sudden plague of millions of spiders is about to be unleashed, to destroy entire countries! The Spider Drow have secretly allied with Evermeet, the dwarven nations, and great forces from Realmspace, and both are preparing for total war against the drow of Lolth!
Given the level of paranoia, plotting, scheming, conniving, and general anarchy within the Forgotten Realms, it is extremely easy to create a Tempest in a Teapot. Nevermind that there are a dozen actual real tempests in progress, which might or might not be aggravated into full blown messes by this sudden change in drow behavior.
But to work, it always needs a tinge of good humor. Always.
