Trying to issue a SELECT against system tables give this error:

SELECT * FROM SYSTEM.TABLE;                                    
*+ Status = -4       SQLSTATE = 5000J        Messages follow:  
*+ DB001036 T50 C-4M321: Table TABLE definition/DB out of sync

In general, IDMS does not use synchronization stamps for system tables, so how is this error possible?

The cause of this problem is most likely that the STAMP BY settings on the catalog definition are incorrect.
DDLCAT and DDLCATLOD should be STAMP BY AREA.
DDLCATX should be STAMP BY TABLE.

This is documented in Defining New Catalog Components.

Release : 19.0
Component : CA IDMS/DB SQL Option

Some level of synchronization stamps are used, even for system tables.
The FORMAT FILE and the adding of the TABLEDDL source member creates synchronization stamps according to the required STAMP BY settings.
If those STAMP BY settings are specified incorrectly in the DMCL, the DB001036 is possible.

Note that if the STAMP BY settings are incorrect at the time the catalog is being created, the TABLEDDL job will fail anyway.
Therefore, the only way for this problem to occur is for the catalog segment and DMCL to be changed after the catalog was originally created.