My perspective is that, for best effect, they should not only be both of them, they should not only be additive, they should also be logically assembled. D&D Worlds are as competitive as the real one, possibly even more so, so a species that has carved itself a niche because of its capacities will tend to keep it and develop a culture around it. And, possibly in fantasy worlds where there is a mythical origin, there is a tie in to that. Tolkien had it for its races and the cultures that derived from it. And if a species race has no natural habitat but is rejected from everywhere else because all the good spots are taken - meaning that it does not have inborn competitive advantage, then it would affect its culture as well (and it might be different cultures depending on where it ends up settling..
After that, the extent to which the players are actually using the material provided to them by the race/culture/etc. is entirely up to them and their preferences. But I would like to point out that the races inborn capabilities have at least a chance to remain in play even with a player that does not care much about the fluff, and at least it would provide some variety and make the character consistent with the race, and therefore at least partially with the culture if the two are reasonably derived from each other.
E.g., once more, in RQ, a player might be wanting to play a dark troll because of its powers, but the way it's built technically would at least draw him towards at least something a bit trollish, just because the dark troll is physically powerful, has dark sense and is connected to the Darkness rune.
I think that logically assembled and leaving options open are a bit contrary choices - there's a binary where you can either have plenty of options to tweak and twist the system, or you can have a very specific campaign world that sets the assumptions about different peoples locked in.
D&D cannot by its default be the latter or it would cease to be D&D, it would be an individual fantasy game. It's also bad at replicating the needs of an individual fantasy world; when you don't have to accomodate so many different playstyles and worldbuilding choices, you can really dial in the mechanics of the game to suit your particular game-world needs.
The issue we're facing is that D&D ORIGINATED as a game in the 1970s with a very specific mechanical system to represent a very specific fantasy world view that, while not confined to a single campaign setting, was confined to very closely akin settings that could easily be stacked into the same world. There's still a place for Blackmoor in the World of Oerth, after all. In Mystara, too.
These were different "worlds" but they had the same baseline assumptions and the rules were written to meet those baseline assumptions. But along the way, the assumptions broadened. It's basically impossible to play a Birthright campaign in 5e currently, because we don't have the tools to do so and playtesting those tools would take a long time. The assumptions are just so different that it's ALMOST a different game altogether from D&D proper. But it's compatible. Birthright would likely be better suited with its own mechanics as a tabletop game divorced from D&D. Dark Sun too - it's got so many assumptions that break the mold that D&D's core rules and assumptions are not really compatible with the world. Ravenloft fits into this category of settings too.
I'm not saying they SHOULDN'T be D&D. They should be. But that's because what D&D IS in terms of setting assumptions has broadened immensely. And when you broaden like that, you need to be ready for all circumstances and not lock players into the assumptions of one world.
That's why we have this new text in the PHB reprints for Drow:
The cult of the god Lolth, Queen of Spiders, has corrupted some of the oldest drow cities, especially in the worlds of Oerth and Toril. Eberron, Krynn, and other realms have escaped the cult’s influence—for now. Wherever the cult lurks, drow heroes stand on the front lines in the war against it, seeking to sunder Lolth’s web.
The culture of Lolth's cult dominates Greyhawk and Toril, but not Eberron, Krynn, etc. Your campaign world might have heroic Drow as the norm but they're suggesting that the cult is likely present there too, or seeking to cross-over to your Material Plane to take over the Drow there too. Seeing as Lolth rules from the Demonweb Pits in the Abyss and most worlds have active connections to the Great Wheel, this is more likely than it seems. Maybe not for Athas, Krynn, or Eberron, but your home plane may just use the Great Wheel as an assumption. And if so, you should consider as a DM having the Cult of Lolth exist in your world, seeping over through the Abyss to your Material Plane. But it need not be the assumption. It's an evil culture, not a lineage trait of evil.
