I've wondered the same thing! I'm curious to see the responses. Here are some examples...
from The Prologue: Concerning Hobbits:
... "It is plain indeed that in spite of later estrangement Hobbits are relatives of our: far nearer to us than Elves, or even than Dwarves. Of old they spoke the languages of Men, after their own fashion, and liked and disliked much the same things as Men did."
from The Passage of the Marshes:
... "'I saw them: grim faces and evil, and noble faces and sad. Many faces proud and fair, and weeds in their silver hair. But all foul, all rotting, all dead. A fell light is in them.' Frodo hid his eyes in his hands. 'I know not who they are; but I thought I saw there Men and Elves, and Orcs beside them.'
... 'Yes, yes,' said Gollum. 'All dead, all rotten. Elves and Men and Orcs. The Dead Marshes. There was a great battle long ago, yes, so they told him when Sméagol was young, when I was young before the Precious came. It was a great battle. Tall Men with long swords, and terrible Elves, and Orcses shrieking.'"
Then a race is used with both caps and no caps in the same paragraph!
from The Black Gate Is Closed:
..."Then he knew that the hope that had for one wild moment stirred in his heart was vain. The trumpets had not run in challenge but in greeting. This was no assault upon the Dark Lord by the men of Gondor, risen like avenging ghosts from the graves of valour long passed away. These were Men of other race, out of the wide Eastlands..."