Hmmm.....

So, if a state employee of California kills a self-professed anarchist, can they claim immunity from prosecution, claiming they were compelled to do so by their state, due to the mandated loyalty oath?

Since all those civil servants signed a loyalty oath to defend the U.S. constitution, can they be summarily drafted into the CA National Guard and sent to Iraq, in order to fulfill their oath?

Just wondering.

Short answer: the loyalty oath is just another feel-good piece of junk passed by legislators who were afraid to vote against something just because it was a dumb idea. They, more than other people, don't want to appear in any way disloyal.

Your first question poses an interesting but unrealistic situation, except that someone professing or even shouting about anarchism is no real danger to the state or the nation. Even in the hypothetical case of someone doing something that poses a real danger to the state of Cal-ee-forn-yuh, it's still a police matter.

Absent some sort of actual military draft, no one can be summarily inducted. The national guard is like all of our armed forces, a volunteer organization. The members who joined because of the educational benefits and the recruiters who promised "just one weekend a month, and two weeks a year" should have read the fine print before siginig up.