It's not in 5e lore, though. Larian made it up.
Thats how lore is made pal, someone made it up ... and WoC approves it as canon.
But yeah, whether Lloth followers or not, it is common for Drow to have red eyes, but they can also have blue, white, pink, purple, silver...and it doesn't matter who they serve.
I believe you are messing two things up here ...
And its race and worshiping.
Feel free to corect me if im wrong, but Llolth-sworn Drow seem to be to be simply Drow who was born inside society of followers of Llolth ... was raised in her image, and know all thing that such Drow should know ... we can expect that s/he would have Llolth-sworn mentality bcs of those things, but its not a rule, since individuality is still possible.
And s/he have red eyes, since Llolth claimed his soul when s/he was born, as mentioned previously.
No matter if s/he personaly do, or do not trully worship Llolth when adult, and responsible for his own believes.
Then there are Seladine Drow ... wich can be translated as "the others" ... meaning any Drow that was not born into Llolth-sworn society ...
And they do have all other eye collors.
Of course all surface dwellers will simply tell you exactly what you said: "it is common for Drow to have red eyes, but they can also have blue, white, pink, purple, silver..."
But surface dweller hardly knows all social groups between Drows.
