There's a significant fallacy in your question, in that being literate is not related to being bilingual or multilingual. Plenty of people currently in the world grow up in multilingual contexts and are competent in two or more languages, without necessarily being literate.

For a classical example, educated Romans, generally speaking, were functionally bilingual in Greek. This was a product of an education system that put high value of mastery of the Greek language and literature.

So, no, multilingualism is not a recent phenomenon. Anywhere you get an overlap of two language populations you will generally get some bilingual speakers.

The medieval German knight Oswald von Wolkenstein travelled through the entire known world of the day^1, served as an ambassador, interpreter and soldier, spoke more than seven languages^2 and has been completely illiterate^3.

1: see his poem "durch Barbarei Arabia". We have dug up materials proving he indeed, for instance, served as an ambassador between Ferdinand I. of Aragon and the antipope Benedict XIII. in Avignon, took part in the siege of Ceuta against the moors and received a monthly wage of 300 gulden from the king of Hungary.

2: as he says (and proves) in his "polyglot poem"

3: see "Konnte Oswald von Wolkenstein Lesen und Schreiben" by George Fenwick Jones.

It was pretty common in the past for a number of reasons.

1. Peasants and authority figures often spoke so differently that they were pretty much speaking different languages. For example, in Carlo Ginzburg's book 'The Cheese and the Worms' the peasant studied speaks Friulian as his native language but testifies in Latin. Anyone wanting to deal with authority in a peasant community would have had to do the same.
2. Aristocratic people have also spoken in multiple languages throughout history, vernacular and clerical/international. Think of all the letters from medieval kings in Latin when they would have spoken various court dialects to their families and servants.
3. Liturgical languages were needed across wide swathes of the world for participation in many of the most important jobs. For example, in medieval Iran you would need to speak Arabic to be involved in bureaucracy despite everybody around you speaking Persian. You couldn't get legal or religious texts in translation for some time.