The following programs are defined by RDO as CONCURRENCY (THREADSAFE).
HBIAST02
HBR$DCW
HBR$DJSE
HBR$SI56
Any issue with changing CONCURRENCY (REQUIRED)?
CICS, Z/OS
Coding CONCURRENCY (REQUIRED) will be fine. The current CICS's RDO definition for the CONCURRENCY setting also is fine as is.