Do I still need to disable or drop column store index before insert and/or update on big tables? As the title says, I thought that from MSSQL 2016 I don't really have to drop or disable ColumnStore indexes before ETL and rebuild it after. 

Any consensus?
Correct, you don't have to.  

For inserts be sure that ETL is saving data directly into compressed rowgroups, not the delta store.

If you want to update or delete data you need to be aware of the internal implementation of the updates on the column store. During DML operations data in a compressed column store rowgroup are never deleted or modified but just flagged as deleted. Updates are implemented as Insert/Delete.
Rows are physically deleted only during index reorg or rebuild.