(Original post by Mathemagicien)
In the West, the riders of Rohan are described as pale skinned and yellow haired. Minas Tirith is the 'white' city. Aragorn refers to his army as the "Men of the West". We have blond haired, blue eyed, tall elves, who are portrayed as 'pure' and 'good'.
Well for starters the only consistent description for elves is tall and pale. They're meant to look vaguely other worldly and an easy visual way of describing that is unnaturally pale but you can drop the Aryan implication. Elrond is one of the most powerful elves in middle earth and is dark haired.
The White City is called such because it is made out of white stone, so not even referencing race with that one.
Aragorn calls his army "the men of the west" because they're the armies of men belonging to the western nations. The last alliance that fought Sauron was simply called the "Last Alliance"
In the East, we have Mordor. The men from the East who came to serve Sauron are dark skinned, from the east and south, and ride elephants. the wild men of the hills are described as "dark", with "dark faces... black eyes and long black hair, and gold rings in their ears... very cruel wicked men they look".
Aside from the comment about the wild men looking cruel, very little states that the men fighting for Sauron are evil in anyway, and the few that are get attribted to Sauron's manipulations rather than inherent racial evilness. They're simply fighting for Sauron who is also called "the Deceiver" and whom was also in the process of manipulating the leaders of both Gondor and Rohan. Quite a lot of the kingdoms of men entreat for peace after the war of the ring. Additionally when you have a race of supernatural pale people like the elves, dark skinned can simply mean tanned, for instance Aragorn is described as lean, dark and tall, with shaggy dark hair.
The orcs are described as "a dark band... swart, slant-eyed"; Orcs are bred to be bad, they have no choice. The evil wizard Saruman tells us that they are elves corrupted by a kind of genetic modification program. They deserve no mercy.
The line describing orcs appearance is about the only thing that supports your assertion, but you spend more time re-iterating their supposed origin in the films (which isn't their actual origin) than capitalising on this.
The Númenóreans of Gondor fell because of a supposed need for racial purity, especially concerning the ancestry of their king, and grew weaker as a result.
Gandalf states, in the extended version of the film, that "The old wisdom that was borne out of the West was forsaken. Kings made tombs more splendid than the houses of the living and counted the names of their descent dearer than the names of their sons. Childless lords sat in aged halls musing on heraldry or in high, cold towers asking questions of the stars. And so the people of Gondor fell into ruin. The line of Kings failed, the White Tree withered, and the rule of Gondor was given over to lesser men."
Nothing in this section refers to racial purity, the passage is basically saying that the Kings forgot that their job was to care for their kingdom and it all went to ****, wasting their time and wealth on needless extravagances and useless endeavours.
The most racism you can accuse Tolkein of is stereotyping, even then he's not advocating discrimination he's simply using symbolism. This is unsettling to a modern audience but you're argument basically is trying to argue that because some of his villains were described a certain way he was a white supremacist which is ludicrous.