The differences between Middle-earth beings may not look like the differences between people in our world. In fact, they're much more stark. Nevertheless, the interactions between all these creatures in The Two Towers—humans, elves, hobbits, and orcs—remind us of race relations in our world, too. It's clear from the get-go that these characters use race as a way to identify each other. But the race of their fellows also creates certain expectations; elves are good, hobbits are inexperienced, orcs are evil, men are proud. Are these fair assumptions? Probably not, but in any case, all of Middle-earth seems to share them.
Tolkien's depiction of the groups of Middle-earth is racist. The differences between the peoples of Middle-earth, which he describes as inherent, suggest unfair prejudice.
In The Two Towers, one of the central distinctions between good peoples like elves or Ents and bad peoples like the orcs is that the good folk can work together in a common cause while the evil folk cannot overlook their differences long enough to cooperate productively.