Why does Tom Hanks pronounce "stupid" as "st-you-pid" in "The Bonfire of the Vanities"?

A yod is another name for the sound/j/, the first sound in the word yes.

Very many varieties of English have a yod in the word stupid. For example, the transcription for stupid given by the Cambridge English Dictionary is:

• /ˈstjuː.pɪd/ ("styoopid")

For many speakers there will be coalescent assimilation between the /t/ and the /j/ giving the following pronunciation:

• /ˈstʃuː.pɪd/ ("schoopid")

The /tʃ/ here is the same sound that we find at the beginning of the word chip.

In most but not all varieties of American English, this yod has disappeared from the word. There are very many words which have lost their yods over the last century or so in American English, but which retain them in other varieties including Southern Standard British English. These yods have become dropped chiefly in words beginning with alveolar consonants /t, d, n, l, s, z/. So for example for many Americans the word news is pronounced: /nuːz/, "nooze" whereas SSBE speakers say:/njuːz/ "nyooze".

So, in fact we could kind of turn the Original Poster's question on its head. It's not a question of where this yod came from, it's a question of where all the other ones went! It seems just that Hanks' character speaks a variety of English where the original yod is still present.

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This blog on yod-dropping may interest readers.