PostgreSQL 10.6 (Ubuntu 10.6-1.pgdg18.04+1) on x86_64-pc-linux-gnu, compiled by gcc (Ubuntu 7.3.0-27ubuntu1~18.04) 7.3.0, 64-bit */
To reproduce, try the below code. Uncomment the alter table line and the error is gone as expected. I would expect the identity should not be need to be defined on a temp table since it won't be replicated anyway.
BEGIN;
CREATE publication test1 FOR ALL TABLES;
CREATE TEMP TABLE testing123 ON COMMIT DROP AS ( SELECT 1 AS value );
/* ALTER TABLE pg_temp.testing123 REPLICA IDENTITY FULL; */
UPDATE testing123 SET value = 2;
/*OUTPUT: ERROR: cannot update table "testing123" because it does not have a replica identity and publishes updates */