Hi Nitin,
A stuck thread is a WebLogic diagnostic. There is a WebLogic setting StuckThreadMaxTime that defaults to 600 seconds. A thread executing for more than this duration will be marked as STUCK. It does not necessarily mean that it is stuck such as in a deadlock, but merely the thread has been executing for longer than the StuckThreadMaxTime setting. In general it is better to think of it was a slow thread. In nearly all support cases the cause has been traced to the database side, where the middleware server is awaiting a query response from the database. This seems to match with your description of RMAN parallelism, although long-running background jobs is also a common cause.
You indicated that the environment went down due to this. How long does the backup typically take? Do the stuck threads automatically resolve after the backup completes? Are you able to move the backup to an offtime / non-peak schedule? Perhaps you could check with a database administrator whether the database server has enough performance and resources to mitigate the issue.
FYI In IFS Cloud the middleware tier no longer uses WebLogic so reports of stuck threads has greatly diminished as customers transition to IFS Cloud.
Best regards -- Ben