How can I automatically alphabetize folders within the Notes app on the Mac?

No such option exists in Notes app. You can only alphabetize notes within a folder.

Let Apple know you would like to see this feature added in an update.

You can request features, point out bugs, etc, at Apple Feedback pages.

http://www.apple.com/feedback/

Is it not?

View > Sort Folder By > Title

Oh, it isn't. That should be renamed Sorts Folder Contents By

On my OS X Notes.app, the folders are listed alphabetically by default when created and I can screw them up is to move them by dragging each one. There is no actual Sort Folder By feature.