If you have an EAR with more than one WAR, you can only extend ResteasyJacksonProvider in one of those WARs.
If both WARs try to include a ResteasyJacksonProvider, then whichever WAR's RESTful service you hit first works and the other fails with a RuntimeException:
org.jboss.weld.exceptions.IllegalArgumentException: WELD-001324 Argument bean must not be null