What is the minimum width I can use for an under-sink cabinet when using a 30" wide cast iron sink?
My off-the-cuff answer is 33" minimum but 36" highly recommended.
But the correct answer is: Get the installation manual for the sink. Usually available online, and if it isn't then contact the manufacturer. The installation manual will show you how much space is needed, particularly how much clearance is needed under each side of the sink, which will vary depending on how it is mounted. Keep in mind that some cabinets will have thicker walls and/or framing pieces under the left and right sides than others.
It is possible that a 33" cabinet might be 1" thick on each side and leave you with 31" of usable space. Combined with a 30" sink that needs no extra space underneath (i.e., it is drop-in and secured entirely on top), you would be just fine. On the other hand, a cabinet that ends up with less usable space (I wouldn't go down to exactly 30" for sure) or a sink that requires mounting brackets underneath the left and right edges will certainly need a wider cabinet.