diff --git a/src/backend/commands/repack_worker.c b/src/backend/commands/repack_worker.c
index b17edd771e2..c40f8c98e06 100644
--- a/src/backend/commands/repack_worker.c
+++ b/src/backend/commands/repack_worker.c
@@ -106,8 +106,9 @@ RepackWorkerMain(Datum main_arg)
 	pq_set_parallel_leader(shared->backend_pid,
 						   shared->backend_proc_number);
 
-	/* Connect to the database. */
-	BackgroundWorkerInitializeConnectionByOid(shared->dbid, shared->roleid, 0);
+	/* Connect to the database. LOGIN is not required. */
+	BackgroundWorkerInitializeConnectionByOid(shared->dbid, shared->roleid,
+											  BGWORKER_BYPASS_ROLELOGINCHECK);
 
 	/*
 	 * Transaction is needed to open relation, and it also provides us with a
@@ -214,7 +215,6 @@ repack_setup_logical_decoding(Oid relid)
 	/*
 	 * Make sure we can use logical decoding.
 	 */
-	CheckSlotPermissions();
 	CheckLogicalDecodingRequirements(true);
 
 	/*
diff --git a/src/test/modules/test_plan_advice/t/001_replan_regress.pl b/src/test/modules/test_plan_advice/t/001_replan_regress.pl
index 38ffa4d11ae..452b179a665 100644
--- a/src/test/modules/test_plan_advice/t/001_replan_regress.pl
+++ b/src/test/modules/test_plan_advice/t/001_replan_regress.pl
@@ -18,6 +18,7 @@ $node->init();
 # Set up our desired configuration.
 $node->append_conf('postgresql.conf', <<EOM);
 shared_preload_libraries='test_plan_advice'
+wal_level=replica
 pg_plan_advice.always_explain_supplied_advice=false
 pg_plan_advice.feedback_warnings=true
 EOM
diff --git a/src/test/regress/expected/cluster.out b/src/test/regress/expected/cluster.out
index 6127b215a86..71270134985 100644
--- a/src/test/regress/expected/cluster.out
+++ b/src/test/regress/expected/cluster.out
@@ -543,7 +543,7 @@ ERROR:  REPACK (CONCURRENTLY) is not supported for partitioned tables
 HINT:  Consider running the command on individual partitions.
 DROP TABLE clstrpart;
 -- Ownership of partitions is checked
-CREATE TABLE ptnowner(i int unique) PARTITION BY LIST (i);
+CREATE TABLE ptnowner(i int unique not null) PARTITION BY LIST (i);
 CREATE INDEX ptnowner_i_idx ON ptnowner(i);
 CREATE TABLE ptnowner1 PARTITION OF ptnowner FOR VALUES IN (1);
 CREATE ROLE regress_ptnowner;
@@ -552,6 +552,8 @@ ALTER TABLE ptnowner1 OWNER TO regress_ptnowner;
 SET SESSION AUTHORIZATION regress_ptnowner;
 CLUSTER ptnowner USING ptnowner_i_idx;
 ERROR:  permission denied for table ptnowner
+ALTER TABLE ptnowner1 REPLICA IDENTITY USING INDEX ptnowner1_i_key;
+REPACK (CONCURRENTLY) ptnowner1;
 RESET SESSION AUTHORIZATION;
 ALTER TABLE ptnowner OWNER TO regress_ptnowner;
 CREATE TEMP TABLE ptnowner_oldnodes AS
@@ -560,6 +562,11 @@ CREATE TEMP TABLE ptnowner_oldnodes AS
 SET SESSION AUTHORIZATION regress_ptnowner;
 CLUSTER ptnowner USING ptnowner_i_idx;
 WARNING:  permission denied to execute CLUSTER on "ptnowner2", skipping it
+-- still can't repack without a replica identity
+ALTER TABLE ptnowner1 REPLICA IDENTITY DEFAULT;
+REPACK (CONCURRENTLY) ptnowner1;
+ERROR:  cannot process relation "ptnowner1"
+HINT:  Relation "ptnowner1" has no identity index.
 RESET SESSION AUTHORIZATION;
 SELECT a.relname, a.relfilenode=b.relfilenode FROM pg_class a
   JOIN ptnowner_oldnodes b USING (oid) ORDER BY a.relname COLLATE "C";
@@ -570,6 +577,15 @@ SELECT a.relname, a.relfilenode=b.relfilenode FROM pg_class a
  ptnowner2 | t
 (3 rows)
 
+SELECT a.relname, a.relfilenode=b.relfilenode FROM pg_class a
+  JOIN ptnowner_oldnodes b USING (oid) ORDER BY a.relname COLLATE "C";
+  relname  | ?column? 
+-----------+----------
+ ptnowner  | t
+ ptnowner1 | f
+ ptnowner2 | t
+(3 rows)
+
 DROP TABLE ptnowner;
 DROP ROLE regress_ptnowner;
 -- Test CLUSTER with external tuplesorting
diff --git a/src/test/regress/parallel_schedule b/src/test/regress/parallel_schedule
index 288e94dc408..5d4f910155e 100644
--- a/src/test/regress/parallel_schedule
+++ b/src/test/regress/parallel_schedule
@@ -102,7 +102,7 @@ test: publication subscription
 # Another group of parallel tests
 # select_views depends on create_view
 # ----------
-test: select_views portals_p2 foreign_key cluster dependency guc bitmapops combocid tsearch tsdicts foreign_data window xmlmap functional_deps advisory_lock indirect_toast equivclass stats_rewrite graph_table
+test: select_views portals_p2 foreign_key dependency guc bitmapops combocid tsearch tsdicts foreign_data window xmlmap functional_deps advisory_lock indirect_toast equivclass stats_rewrite graph_table
 
 # ----------
 # Another group of parallel tests (JSON related)
@@ -128,7 +128,7 @@ test: partition_merge partition_split partition_join partition_prune reloptions
 # ----------
 # Another group of parallel tests (compression)
 # ----------
-test: compression compression_lz4 compression_pglz
+test: compression compression_lz4 compression_pglz cluster
 
 # event_trigger depends on create_am and cannot run concurrently with
 # any test that runs DDL
diff --git a/src/test/regress/sql/cluster.sql b/src/test/regress/sql/cluster.sql
index d14063a9683..6746236ffec 100644
--- a/src/test/regress/sql/cluster.sql
+++ b/src/test/regress/sql/cluster.sql
@@ -254,7 +254,7 @@ REPACK (CONCURRENTLY) clstrpart;
 DROP TABLE clstrpart;
 
 -- Ownership of partitions is checked
-CREATE TABLE ptnowner(i int unique) PARTITION BY LIST (i);
+CREATE TABLE ptnowner(i int unique not null) PARTITION BY LIST (i);
 CREATE INDEX ptnowner_i_idx ON ptnowner(i);
 CREATE TABLE ptnowner1 PARTITION OF ptnowner FOR VALUES IN (1);
 CREATE ROLE regress_ptnowner;
@@ -262,6 +262,8 @@ CREATE TABLE ptnowner2 PARTITION OF ptnowner FOR VALUES IN (2);
 ALTER TABLE ptnowner1 OWNER TO regress_ptnowner;
 SET SESSION AUTHORIZATION regress_ptnowner;
 CLUSTER ptnowner USING ptnowner_i_idx;
+ALTER TABLE ptnowner1 REPLICA IDENTITY USING INDEX ptnowner1_i_key;
+REPACK (CONCURRENTLY) ptnowner1;
 RESET SESSION AUTHORIZATION;
 ALTER TABLE ptnowner OWNER TO regress_ptnowner;
 CREATE TEMP TABLE ptnowner_oldnodes AS
@@ -269,7 +271,12 @@ CREATE TEMP TABLE ptnowner_oldnodes AS
   JOIN pg_class AS c ON c.oid=tree.relid;
 SET SESSION AUTHORIZATION regress_ptnowner;
 CLUSTER ptnowner USING ptnowner_i_idx;
+-- still can't repack without a replica identity
+ALTER TABLE ptnowner1 REPLICA IDENTITY DEFAULT;
+REPACK (CONCURRENTLY) ptnowner1;
 RESET SESSION AUTHORIZATION;
+SELECT a.relname, a.relfilenode=b.relfilenode FROM pg_class a
+  JOIN ptnowner_oldnodes b USING (oid) ORDER BY a.relname COLLATE "C";
 SELECT a.relname, a.relfilenode=b.relfilenode FROM pg_class a
   JOIN ptnowner_oldnodes b USING (oid) ORDER BY a.relname COLLATE "C";
 DROP TABLE ptnowner;