This is a difficult question. In the film, A Time to Kill, written by John Grisham, I believe that religion can be seen in different places, with different effects.
First of all, Carl Lee Hailey, the father of the young black girl who was raped, beaten and left for dead, is a God-fearing man. It is certain that taking the lives of two men is not something that he would have considered under any other circumstances, but for his daughter's near-death, and the good possibility that in the racist community of which they are a part the men will go free, Carl Lee is ready to sacrifice himself to avenge his daughter's attack.
Some people may not be aware that the KKK (Klu Klux Klan) was made up of predominantly Protestant [white] men. The KKK...
...made frequent reference to America's "Anglo-Saxon" and "Celtic" blood, harking back to 19th century nativism and racialism priding themselves on being descended from the original 18th century British colonial revolutionaries...
In reaction to social changes, the Klan adopted anti-Jewish, anti-Catholic, anti-Communist and anti-immigrant slants....
When the organizer was done with an area, he organized a huge rally, often with burning crosses and perhaps presented a Bible to a local Protestant minister
This is an aspect of religion within the story that would have been behind the scenes, looking directly to the members of the Klan who wanted Carl executed. They used all kinds of intimidation for anyone who supported Hailey including burning down Jake's house, threatening, Ellen Roark physically, and even Jake's secretary, Ethel, and her husband, who later dies from the assault.
In another portion of the film, the NAACP wants to represent Carl, and they try to use the influence of Carl's pastor to get Carl to change his mind. Carl realizes that this will be of no benefit to him or his family, which is what his pastor should be thinking about. The NAACP and his pastor are more interested in making headlines. Carl decides to take his chances with Jake, even though Jake has no inkling, as a southern white male what it means to be black in the South.
This last example or religion's place is probably the most relevant to the plot. The support a church-going man might hope to expect from his congregation is not there. (As seen with the church's support of Tom Robinson in To Kill a Mockingbird.) His family is not being provided for, and Carl's family is everything to him, not the agenda his pastor and the NAACP. Religion does not, in this instance, do anything to help Carl's case.
Religion does not play a major role in the film's developments. The racism in the Mississippi Delta setting of the film is a part of the social setting. To this end, one could say that religion has not assisted the pursuit of justice. True religious tenets could not embrace the racial discrimination that is present in the area. The fact that Hailey approaches Brigance with fear that justice will be denied to his family reflects that religious worship has not assisted with ensuring that justice could be received by all the citizens in the area. While religion is not the reason for the racism in the region, it is not helping to defuse it. Brigance's closing argument about the girl being raped, punctuated with "Imagine if she was white," brings to light that religion and other social forces have not alleviated the strongly racist element present in the setting. In such a realm, justice is in peril, indicating that religion might not have done its part to help to pursuit of justice for all individuals.