There are others in-game that have the eye-color shift, that don't worship the seldarine:
Viconia (actually accurate to her portraits from the original saga) and Sendai
So that can't be the reason. It seems that just renouncing Lolth is enough?
But that's all to the side of the real weirdness, which is that the eye-color changing thing is a thing at all in the game. Like drow are well known for their red eyes in all previously published material, and there are other established eye colors among the drow....but there's absolutely zero correlation between eye color and worshipping/not worshipping the spider queen. There are tons of Lolth-worshipping drow with non-red eyes in canon previously.
It's just a very peculiar retcon Larian introduced that serves no real purpose other than to (messily) distinguish Lotlh's followers from the rest (which itself doesn't really serve a purpose).