So, here's what I *think* may be happening...
If I am understanding correctly, you've deleted the composer tag in the file, but when you 'update library from tags' the library retains the existing composer tag. This would be by design. While it doesn't suit your current workflow, there will be other scenarios where this would not be the desired behaviour, and somewhere along the dev curve, that was the one that came out on top. Here's how to test my theory...
Take two files, one where you would like composer retained (and you already have it in the file tag), and one where you want the composer to be cleared (and you already have it empty in the file tag), and clear the composer field for both files in MC. Then do an 'update library from tags' on both files. One should bring in the composer, the other shouldn't.
If that is the case, then you should be good to select all files, clear the composer field, then update from tags, on the lot, at the same time.
Or...
If you're happy that the composer tags for all your "Classical" genre tagged files are good in MC and the file tags, and you know that the rest do not have composer tag set, you could just select all files that are not "Classical", clear the composer tag in MC, and if my theory and understanding is correct, the library and the file tags should then be in sync and you're good to move on to another project.
-marko