C.F., in other word, "Ethnic Reputation", is virtually hidden and specific to each race available in the game. It decreases if you kill enemy of respective race / ethnicity. Increases by having your unit defeated in the battle (not perished), this method will drop their own loyalty, though. You can check your C.F. by recruiting new unit from shop. Their current loyalty represents your C.F. of their race. Upon conquering the 100th floor of Hellgate, you can access the Chaos Frame page in Warren Report and read your exact C.F. statistic of each race.
In order to suppress the drop of C.F., try to kill only enemies of "unknown" race (all else besides Human and Hawkman's race is unknown) or the leader if the battle objective is not "defeat all enemies". Persuade enemy of known race. Some choice throughout the story also affects the C.F., the more peaceful the better.