JBoss EAP fails to start server instances in domain mode when the JVM is running in FIPS mode

Issue

Why does JBoss fail to start server instances in domain mode when the JVM is running in FIPS mode?

I see the following error when the domain is starting and JBoss appears to hang:

    [Server:server-one] 16:01:36,249 ERROR [org.jboss.msc.service.fail] (MSC service thread 1-3) MSC000001: Failed to start service jboss.host.controller.client: org.jboss.msc.service.StartException in service jboss.host.controller.client: java.io.IOException: JBAS015847: Unable to initialise a basic SSLContext 'FIPS mode: only SunJSSE TrustManagers may be used'
    [Server:server-one]     at org.jboss.as.server.mgmt.domain.HostControllerConnectionService.start(HostControllerConnectionService.java:132) [jboss-as-server-7.5.4.Final-redhat-4.jar:7.5.4.Final-redhat-4]
    [Server:server-one]     at org.jboss.msc.service.ServiceControllerImpl$StartTask.startService(ServiceControllerImpl.java:1980) [jboss-msc-1.1.5.Final-redhat-1.jar:1.1.5.Final-redhat-1]
    [Server:server-one]     at org.jboss.msc.service.ServiceControllerImpl$StartTask.run(ServiceControllerImpl.java:1913) [jboss-msc-1.1.5.Final-redhat-1.jar:1.1.5.Final-redhat-1]
    [Server:server-one]     at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1142) [rt.jar:1.8.0_60]
    [Server:server-one]     at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:617) [rt.jar:1.8.0_60]
    [Server:server-one]     at java.lang.Thread.run(Thread.java:745) [rt.jar:1.8.0_60]
    [Server:server-one] Caused by: java.io.IOException: JBAS015847: Unable to initialise a basic SSLContext 'FIPS mode: only SunJSSE TrustManagers may be used'
    [Server:server-one]     at org.jboss.as.server.mgmt.domain.HostControllerConnectionService.getAcceptingSSLContext(HostControllerConnectionService.java:207) [jboss-as-server-7.5.4.Final-redhat-4.jar:7.5.4.Final-redhat-4]
    [Server:server-one]     at org.jboss.as.server.mgmt.domain.HostControllerConnectionService.start(HostControllerConnectionService.java:111) [jboss-as-server-7.5.4.Final-redhat-4.jar:7.5.4.Final-redhat-4]
    [Server:server-one]     ... 5 more