Tolkien actually said that dwarves were inspired by the Jews and semitic peoples and languages, as well as medieval literature about the Jews. (Yeah, that means that some things about dwarves are rather insensitive when viewed through that light.) The idea that they're Scottish-like is a fan invention. Same thing with Celtic elves, as Tolkien wanted to specifically *exclude* Celtic influence from Middle-Earth. Symbolically speaking, elves are supposed to be people without Catholic original sin.
Orcs? Well, he said some things that indicate they probably come from a combination of wordplay and some unfortunate, wholly unconscious attitudes which he certainly consciously repudiated, but still exist.
I think in practice, the elves as the nobility and orcs as the proletariat works in the context of the story. After all, all that makes Aragorn worthy of being the king of men is that he's half-elf and comes from a long line of human nobility. A human nobility, which, by the way, caused this whole mess in the first place. But because of his bloodline he's worthy of "saving" the world from the evils Sauron represents, like indoor plumbing, so they can be subservient to him and his wife the elf princess in an agrarian society, free to be surfs.
To be sure, other parts can be read as Sauron representing big industry and the message is mainly pro-environmental, this is the message hippies tended to take away from it, and the angle the cinematography in the movies played up. But it's much more pro-elitist than pro-earth.
Contrast this with JK Rowling, where the noble class is portrayed as racist and evil, willing to commit unspeakable horrors to protect their position and birthright. There's not a single rich person in the books who isn't a complete horse's ass. And these rich, racially "pure" nobles get brought down by a couple of poor, "racially-inferior" kids.
I think the problem with saying that racial diversity in D&D comes from demi-humans, well... if your idea of diversity is all different kinds of white people...
The thing is, D&D was created in the 70's. In fact, Chainmail was first published in 1971, seven years after the passing of the Civil Rights Act, and three years after the death of Dr. King. It's from a different time. And the racial ideas need to change.
Example: Angus, Thongs and Perfect Snogging. The books are very thinly veiled auto-biographies of a woman who went to high school in the 1970's. They're very anachronistic in that they're ostensibly set in the present day, but no one has a computer or a mobile. Also, everyone is white. So for the movie, one of the main characters is of Indian descent. Why? Because it's 2008, not 1975.