I hesitate to report this, since the fix will be to my (in game) detriment.
Now that a gameplay update confirms it, it's clear that the intention is that dairy processing is meant to have a time limit, presumable to limit the amount that can be pipelined through a hit of No-No. Mouse interaction is stalled with the "wah-whoa" noise. But, keyboard interaction is not.
Specifically, while shaking milk, it's possible to hit "B" to access inventory, arrow key to another milk and H to shake it as well. The actions queue, so that rather than inhibiting No-no cheesemaking, the result is a rather pleasing avalanche of dairy products when they all finish at the end of the same delay.
My advice: cheesemongers, mong cheese before this gets fixed. :)