There are plenty of database systems (MySQL enterprise, Postgres, Oracle, SQL Server) that support encrypted data-at-rest and there are even more ways to run a DBMS on top of encrypted disks and volumes (dm-crypt, Bitlocker).
Running in the cloud? Amazon AWS provides EBS encryption (and likely more) and Microsoft Azure provides data at rest encryption for all storage types (tables, queues, page and block (disk) blobs) and transparent encryption for Azure SQL Database.
Want more control over the encryption in the cloud? Amazon and Azure both provide HSMs, called CloudHSM and Azure Key Vault, respectively. Azure supports additional encryption at the VM level integrating with Bitlocker and/or DM-Crypt.
There's really no excuse for not having figured out data encryption for customer data and secrets at this point.
Edit: It appears Slack has since updated their security docs and they now use encryption at rest. Good! It's inexplicable to me that anyone would believe that a database index would be incompatible with encryption.