If I understand it correctly, they want to prevent any one faction from claiming victory in the war to prevent an Emperor from rising in cyrodil and so they can maintain a Tamriel where no central power has influence over all the smaller nations.
That's not anarchist or they would be trying to interfere in smaller nations as well, but it is pretty darn based to want to prevent a central authority from having power over the whole continent.
Their methods may be bad but I can totally get behind the idea of their goal.
Playing your character the way your character should play is all that matters. Play as well as you can but never betray the character. Doing so would make playing an mmoRPG pointless.