If you add a field there is no strict requirement on rebuild. Existing indexed documents are given a null value for the new field. On a future re-index, values from source data are added to documents.
While you can't directly delete a field from an Azure Search index, you can achieve the same effect without rebuilding the index by having your application simply ignore the "deleted" field. If you use this approach, a deleted field isn't used, but physically the field definition and contents remain in the index until the next time you rebuild your index.
Changing a field definition requires you to rebuild your index, with the exception of changing these index attributes: Retrievable, SearchAnalyzer, SynonymMaps. You can add the Retrievable, SearchAnalyzer, and SynonymMaps attributes to an existing field or change their values without having to rebuild the index.