Tomcat does not run by default with a security manager enabled; if you turn that on (by using the "-security" switch of the catalina.sh script), it's possible that you'll see the same exceptions.
You should look into the security policy that's used by WebSphere, and see if it can possibly be relaxed.
I've enabled tomcat security: catalina start -security and modified catalina.policy file.
And this policy file has no permissions for "modifyThread" and "modifyThreadGroup":
I permitted everything on WebSphere and Tomcat except "modifyThread" and "modifyThreadGroup".
But axis2 works on Tomcat without any "access denied". And axis2 + WepSphere blames "modifyThreadGroup : Access denied" with the similar policy file.
Tomcat typically gets run under the Sun/Oracle JVM. WebSphere is often run under the IBM J9 JVM. While access rights like the ones mentioned would appear to me to be something both JVMs would support and do so in an identical manner, it's worth checking to make sure that that's not the issue.
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