in inherit the wind what obstacle did cate and drummond had to overcome

Drummond came into this vilified as an atheist. In a religious community such as Hillsboro, that was a dirty word. Cates of course has to overcome a very rigid town steeped in their religion and bent on persecuting "heretics".

Bertram Cates

Bert Cates, age twenty-four, is a "pale, thin young man" ­ "quiet, shy, well-mannered, not particularly good-looking." Cates is in jail at the beginning of the play, arrested and about to go on trial for teaching evolution to his seventh-graders. Despite Rachel's urgings to him to confess, Cates knows he did not do wrong. Unlike most of Hillsboro, he does not see things in black-and-white but understands that the world is complex. His intellectual musings, including the questions about the world he has whispered to Rachel, are turned against him by Brady ­ who sees blasphemy in his questions and observations. A quiet, unassumng young man, Cates is the center of a trial which labels him the destroyer of faith. He is terrified as the jurors return, fearful he will be imprisoned for years. His victory, in a town that no longer wants him, is only a partial victory, but he is proud when Drummond tells him that he has made the way easier for the next man. He is full of admiration for Rachel when she chooses to think, and the two leave happily together when he is released on bail paid by Hornbeck's paper.

Henry Drummond

A famous lawyer, known for his skilled legal defenses, Drummond is hired by the Baltimore Herald to defend Cates. Rev. Brown describes him as a godless man, for his defenses of the guilty, in which he twists the blame onto society and its perceptions. Drummond and Brady were once friends and maintain respect for each other, but each see the other as in the wrong on this case. Drummond believes Brady has moved away from him simply by standing still, by not progressing with the world. Brady says that for forty years, where Brady fights, headlines follow and sees him as a worthy opponent. Physically, he is hunched over, with a head that juts forward, making Melinda mistake him for the devil when he first appears. Drummond's strongest showing in the courtroom stems from desperation, when the court disallows any testimony on evolution and calls Brady as an expert on the Bible. Drummond's belief in the sanctity of ideas and freedom of thought, as well as his knowledge of Brady's weaknesses, allows him to successfully defend Cates' for speaking his thoughts allowed. In the end, he is an atheist who believes in God, as Hornbeck calls him, because of his respect for Brady's convictions and ideals.

If you need a detailed look at the obstacles and themes of the novel follow the link provided below;

http://www.gradesaver.com/inherit-the-wind/study-guide/major-themes/