Eligible voters are permitted to vote in the four General Field categories (Album Of The Year, Record Of The Year, Song Of The Year, and Best New Artist) and up to 15 additional award categories, based on their areas and genres of expertise. In order to preserve the integrity of the voting process, voters are instructed to vote only in those categories in which they are most knowledgeable, passionate and qualified.
There are about a million categories, so cast recording probably doesn't make a lot of people's 15.
And it's actually two rounds of voting by the full membership, rather than a nominating committee. A handful of "craft" categories are determined by committee, and some more of those and about 2/3 of genres (but not Musical Theatre) are reviewed by committees between voting and nominations.