The word isn't as old as you might think
Xenophobia—"fear or hatred of strangers or foreigners"—has the look and feel of a word that has been in the English language for hundreds of years, borne of the tumultuous political climates of the Renaissance and the penchant that many writers back then had for fashioning fancy new words from Latin and Greek. It is not that old. In fact, the word is relatively new (with an emphasis on "relatively"), with all evidence suggesting that it originated near the end of the 19th century. Our earliest citation is from 1880:
Here, however, as in other cases, we are inclined to think that intelligent xenomania is decidedly preferable to the Xenophobia which is of necessity and always unintelligent.
—The Daily News (London, England), 12 April 1880
Xenophobia was formed from a brace of words found in ancient Greek, xenos (which can mean either "stranger" or "guest") and phobos (which can mean either "flight" or "fear"). It appears to have arrived on the heels of another late-19th century coinage, xenomania ("an inordinate attachment to foreign things"), which, sadly, has proved to not have the same currency as xenophobia, and was followed shortly afterwards by the forms xenophobe and xenophobic:
There is a wider field for satire in the behavior of Xenophobes, who wherever they wander say “for all we can see foreigners is ‘mostly fools.’”
—Daily News (London, England), 26 March 1891
Zeikin seems to have been a faithful and conscientious teacher, for even such a fanatical Xenophobe as Theophylactus, Archbishop of Tver, allows that his intentions were at least honest, and his morals unexceptionable.
—R. Nisbet Bain, The Pupils of Peter the Great, 1897
Of course, the fact that the word xenophobia did not exist before Rutherford B. Hayes was president of the United States does not mean that the condition itself was absent. After all, things may very well exist before they are named; additionally, our language did have another word for the hatred or distrust of strangers prior to this (albeit a very obscure one): misoxenie.
Indeed the Genius, and common humour of a Nation, is not easily alterable, and our Misoxenie (or hatred to Strangers) was no new quality, for Horace noted it before or about Christs birth and Englishmen can hardly see when they are well to keepe them to.
—John Speed, The Theatre of the Empire of Great Britain, 1611
Lest all this focus of words relating to fear and hatred of strangers proves to be depressing, we should point out that our language also has a fair number of words formed from xenos which are slightly more pleasant. We have xenophile ("one attracted to foreign things") and xenial ("of, relating to, or constituting hospitality or relations between host and guest"), which, although little used, help in some way to balance out our language.