I noticed that clustering can take a long time and lock the table entirely, even for reads.
Index Organized Tables and incremental clustering would be perfect, but sadly they aren't supported by PostgreSQL.
Now I realize that it also lock the replicas' tables, so apparently there isn't a way to cluster without having a lot of downtime?
Setting rds.logical_replication to 1 on both master and replica instances didn't help.
I would like to cluster four big tables every week for better performance.