Racism appears to be a word of recent origin, with no citations currently known that would suggest the word was in use prior to the early 20th century. But the fact that the word is fairly new does not prove that the concept of racism did not exist in the distant past. Things may have words to describe them before they exist (spaceship, for instance, has been in use since the 19th century, well before the rocket-fired vessels were invented), and things may exist for a considerable time before they are given names (t-shirt does not appear in print until the 20th century, although the article of clothing existed prior to 1900).
Dictionaries are often treated as the final arbiter in arguments over a word’s meaning, but they are not always well suited for settling disputes. The lexicographer’s role is to explain how words are (or have been) actually used, not how some may feel that they should be used, and they say nothing about the intrinsic nature of the thing named by a word, much less the significance it may have for individuals. When discussing concepts like racism, therefore, it is prudent to recognize that quoting from a dictionary is unlikely to either mollify or persuade the person with whom one is arguing.