How have US Christian churches handled discrimination and segregation in the past? How did Christian Churches deal with segregation laws in the United States and are there any Bible passages that deals with discrimination and segregation? What were typical responses from Churches that were within that sub-culture? Were there Churches on both sides of the issue?
The doctrinal controversies inherent have been discussed in Does the Bible support slavery and (white) superiority in the context of American slavery?, so I will limit myself to actual movements.  This question: When did the African-American population become Christian? also talks about the rise of the black church.
Perhaps the most famous examples of how the church both engaged in and overcame racism are:

The emergence of the AME Church
The AME Church was founded by Richard Allen, a black minister in Philadelphia in the late 1700s.  Although licensed, his ministry was restricted to blacks, and was relegated to early morning services.  When one prayer meeting went long, the story goes, the whites came in and told him he had to move, even while in the midst of prayer. When he demanded that the prayer should continue, the white men beat him savagely.  This was the genesis for the denomination to begin.

The abolitionist movement, and William Wilberforce
Slavery was abolished in the United Kingdom in 1807, and William Wilberforce is most commonly credited with the legislative victory.  A committed Christian, he understood that God was no respecter of persons, and that in Christ, there is neither Jew nor Greek, Slave nor Free.  The Abolitionist Movement in the United States took largely the same queue.

The emergence of the Civil Rights Movement amongst churches in Alabama
That the Southern Christian Leadership Conference was started by the Reverend Dr. Martin Luther King, Jr. is not a coincidence.  Much of the early organizing against segregation was coordinated in churches in Montgomery, Birmingham, Atlanta, and later across the south.

The Apology By The Southern Baptist Convention for Slavery in 1995.
The largest denomination in the United States outside of the Roman Catholic Church is the Southern Baptist Convention.  It was formed in 1845, as the result of a split between the Northern Baptists and Southern Baptists, over the question of whether or not missionaries should be allowed to keep slaves.  In 1995, the SBC acknowledged this history, and asked forgiveness for it.


The answer to your questions are thus:

The church was on both sides of the issue, perpetuating evil and good in this regard. (I think I can get away with calling discrimination and slavery as evil).
In general, the White church tended to justify itself, but later came around on the issue
The Black church in the US is neglected way too much.