What are the unwritten rules about race that Mr. Gilmer attempts to get Tom to break? Does he succeed? What parts of Tom's testimony would have offended jurors who supported the laws and customs of segregated society?

The answer is explained below

Explanation:

Mr Gilmer insinuates that Tom felt superior to Mayella, suggesting that he, "a Negro field hand," expresses pity for a white woman, and should never be so confident as to feel pity towards a white person, because they believe black men occupy the lowest rung of society.

This offends those who support segregated society because they believe black people are below them.