Embracing diversity (as well as the contrary, wanting more uniformity) might be a bit of a historical constant. You can find it at the very beginning of Confucius' Analects.
Is it not delightful to have friends coming from distant quarters?
John Tzetzes from Constantinople expresses similar sentiments in the 12th century, albeit with a heavy dose of intolerance at the same time:
One finds me Scythian among Scythians, Latin among Latins...
And also to Persians I speak in Persian...
To Alans I say in their tongue:
‘Good day, my lord, my archontissa, where are you from? Tapankhas mesfili khsina korthi kanda, and so on’ . . .
Arabs, since they are Arabs, I address in Arabic...
And also I welcome the Ros according to their habits...
‘Sdraste, brate, sestritza’, and I say, ‘dobra deni’.
To Jews I say in a proper manner in Hebrew:
‘Your blind house devoted to magic, your mouth, a chasmengulfing flies,
Memakomene beth fagi beelzebul timaie..."
I am sure that it is possible to find lots of similar quotes through the centuries.
One example of turning (intra-Christian) diversity into official policies is the Electorate of Brandenburg and later the Kingdom of Prussia during the late 17th and early 18th century, epitomized in Frederick II's famous sentence
Everybody should go to heaven in his own fashion here
(den hier mus ein jeder nach Seiner Fasson Selich werden)
As for the current push for more diversity, it seems to be mainly the logical consequence of women's emancipation and increased international mobility post-WWII. In the US the Black civil rights movement probably also plays a role. Supporting equal rights and non-segregationist policies means, in practical terms, that one should also support more diversity at the workplace.
On a more opportunistic note (one that matches well with Prussian and especially the Constantinopolan examples above), in some places there are very direct advantages from having a diverse team. E.g. when developing or servicing products on a globalized market. So economic globalization and modern communications do play a role as well.