According to this blog, the most widely-held interpretation is that drunken monkeys were simply seen as a fun thing to paint. However, the author argues that there was likely a deeper significance to these paintings; they were, he claims, a kind of early-modern Reefer Madness, meant as social commentary about the dangers of the new drugs that had become available to Europeans, including tobacco, opium, and distilled spirits.
It also has quite a few examples of monkey paintings:
I don't know. The author may simply be reading a modern bias into these paintings.