Ethical formalism is a theory that defines moral judgments based on their logical form, not their content. If Crooks is an ethical formalist, then he bases his moral judgments on ethical laws or universals such as "thou shall not kill." A universal applies anywhere and everywhere. It is hard to say exactly what Crooks' moral philosophy is, but if we were to try to make the argument that Crooks follows an ethical formalist philosophy, there are two things that support this.
First, Crooks is completely isolated from the other ranch hands. He has some interaction with them but he spends most of his time alone. He comments that his main companions are books. In Chapter 4, he even complains to Lennie about how he winds up alone every night with his books, "Books ain't no good. A guy needs somebody-to be near him." Since Crooks spends most of his life alone with books, we might assume that most of his knowledge comes from books, not from practical interaction and experiences with other people. Therefore, the universal laws and moral codes he lives by come from books and his own private thoughts. Since he has limited interaction with other people in the real world, it is hard for him to apply these codes and moral arguments based on the content of real life. He must rely on the formal (logical and semantic) structure of the words he reads.
Secondly, even more in terms of social applications of moral philosophy, Crooks' isolation and loneliness lead him to rely on books not just for moral philosophy but for companionship. In this sense, he is a formalist not by choice but by necessity. And this is a result of the fact that he is not white.
Furthermore, although Crooks believes that he should be treated on equal grounds with the whites, he knows the current state of the social structure won't allow it. He even tries to stand up to Curley's wife, but when she threatens him, he backs down because he knows he could be fired or worse. Crooks reluctantly accepts his second class status, but deep down, he knows that this is an affect of racism. Crooks also knows that this mistreatment is not based on a logical, ethical or formal argument; rather, it is based on actual social traditions which have a history of racism. Therefore, he backs down from Curley's wife because of these social realities. But it is likely that he believes things like "all men are created equal" and "racism is a prejudicial, illogical and unethical practice and belief system." These are both ethical formalist arguments (which could be consequentialist arguments if he did live in a society where all people are treated equally). The very fact that Crooks is treated as an inferior is evidence that the society he lives in follows a different philosophy, one based on a history of slavery and racism.