This paragraph sets out all the influences on Angel Clare's father and his passionate, committed and conservative Christianity.
First, Hardy lists the historic dissidents and protestant church fathers with whom Clare senior has most in common: John Wycliffe, an early advocate of translating the Bible into English; John Huss, who was burned at the stake for spreading views that the Catholic Church regarded as heretical; Martin Luther, who began the Protestant Reformation; and John Calvin, whose theological system rested on the belief that people are helpless to save themselves and can only rely on God's mysterious grace for eternal life. All these men shared a certain fanaticism, a willingness to be persecuted and even die for their convictions, and a contempt for the established practices of the Church of their age.
Next, Hardy lists the New Testament writers whom Mr Clare likes (Paul of Tarsus, St John), dislikes (St James, who is sometimes thought to have been Jesus's brother) and feels ambivalent about (Timothy, Titus and Philemon). Essentially, what these likes and dislikes tell us is that Mr Clare is a great believer in the doctrine of "justification by faith". This is the idea that the good or bad that a person does in their lifetime has no effect on their chance of eternal life, so long as they truly repent of their sins and whole-heartedly believe in God. This explains why Mr Clare is so passionate about converting hardened sinners like Alec D'Urberville.
The reference to the renunciative philosophy of Schopenhauer and Leopardi would no doubt shock Mr Clare, as both thinkers were confirmed atheists. However, what they share with Mr Clare is a scepticism as to the possibility that human beings might make any difference to the world or their ultimate fate by their actions.
Finally, Hardy refers to several sets of religious rules, which Mr Clare variously likes or hates. The Penitential Canons are a set of regulations about the different penances that should be done to atone for various sins. As a believer in justification by faith, it's no surprise that Mr Clare has little time for these. The Rubric sets out the rituals that should be followed in Church services, dictating a degree of formality that is quite at odds with Mr Clares more impulsive and emotional preaching style. The 39 Articles are a set of statements published during the reign of Elizabeth I, which describe the Protestant Faith and the way it should be observed in the world.