AWS RDS: why is there "write IOPS" in my replica instance?

You still have writes from the master node as data is replicated.

Additionally any interactions that use temp tables would perform a local write to disk.

A Postgres database replica contains all of the data storage (tablespaces and other internally-managed files) that are present on the primary instance. The difference is that these data files are updated based on information in the write-ahead log (WAL) rather than user-submitted inserts/updates/deletes.

In addition, as a commenter noted, Postgres also uses temporary tables that may be flushed to disk, even for read-only queries.

In practice, you will need at least as many total IOPS for your replicas as you need for the primary, because the replica will typically be performing IO-intensive queries in addition to the updates received from the primary.