For the Content Feeder this step can be skipped, as it stores its state in the Solr index.

The CAE Feeder stores its state in a dedicated SQL database. This database has to be backed up and it is important to do so before taking the backup of the Solr index.

The reason for this is that if the restored Solr index is newer than the restored CAE Feeder database, the CAE Feeder might feed some index documents once again which is okay, but if the Solr index were older than the CAE Feeder database, index changes between the time of the Solr backup and CAE Feeder backup could be lost.

If your database / tools provide the feature of hot backup, you do not have to stop the CAE Feeder for taking backups.