Since I have been running into this issue lately: JPA does not recommend EntityManager interactions within JPA lifecycle callbacks*. Shouldn't we add a note somewhere that injected resources require special attention regarding JPA compliance? And because of that firing CDI events from a JPA entity listener is particularly dangerous?
In my case I tried to implement global available created/updated/deleted entity events which turned out to be an bad idea if implemented on EntityListener level.
* JPA Spec 3.5.2: In general, the lifecycle method of a portable application should not invoke EntityManager or Query operations, access other entity instances, or modify relationships within the same persistence context. A lifecycle callback method may modify the non-relationship state of the entity on which it is invoked.