It is questionable whether Reginald Rose's 1954 play, Twelve Angry Men, suggests that prejudices are a factor in every conflict. It does, though, certainly argue that racism can be a factor in supposedly impartial jury deliberations.
To a certain degree, and essential to the story for dramatic purposes, Rose's play presents a level of diversity, at least among Caucasian men, that exceeds what would normally occur in a modern jury, in which defense attorneys have an opportunity to screen potential jurors for signs of racial or ethnic prejudice. Having said that, racism certainly can and does play a part in some criminal trials. It is not, however, a factor in all conflicts.
In Twelve Angy Men, there is one particularly virulent racist, Juror #10, who launches into angry tirades regarding Hispanics, the ethnicity of the defendant. In the end, of course, the jury agrees to acquit the defendant when the concept of "innocent until proven guilty" prevails.
Rose's play is important in illustrating the manner in which prejudices can and do afflict the criminal justice system. It is a stretch, however, to conclude that Twelve Angry Men is an indictment of all mankind for the role of race in conflicts in which race may very well not be a factor at all.