+1 to the OP
Race and tags are different things.
It should be possible to make drow a sub race of elf, add a text in character creation "Drow are from the underdark and people will react very different to them than to other elves." and use whatever tags you like.
Also, there should not be two drow races.
One addition from my side.
You write that it is a choice of a char to turn away from the typical drow society. This is true. But drow is a race, not a religion.
There can be drow who were never part of the usual drow society to begin with. There could be drow who were born on the surface. Or some people of another race attacked some drow and those drow had a baby. The attackers did not want to kill the baby and took it with them.
Most drow live in underdark cities and most non drow do not like them. But not every drow started his/her life as lolth worshipper.
There is still no need for different drow races. Other people see that you are a drow, they cannot see your background.
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World leading expert of artificial stupidity.
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