Cherry picking, or "counting the hits and forgetting the misses," refers to the practice of choosing quotes and research which supports ones views while ignoring credible quotes and research, in the same branch of study, which undermines or contradicts ones views. It is often motivated by confirmation bias.
"But I say unto you, That ye resist not evil: but whosoever shall smite thee on thy right cheek, turn to him the other also."
while ignoring the Christian marines' favorite bible quote:
"Think not that I am come to send peace on earth: I came not to send peace, but a sword."
Christians opposed to gay rights often cite Leviticus to support their views:
"Thou shalt not lie with mankind, as with womankind: it is abomination."
Theists often cherry pick which groups to discriminate against without any consistency. For example, certain Christian shop owners refuse to serve gay customers but would serve an adulterer. They argue that adultery is a "different kind of sin", which is special pleading. 
- The Young Turks, Religious Bigot Against Gays But Adultery Is A “Different Kind Of Sin", 3 Apr 2015
- Cafeteria Christian
- Quote mining
- Selective use of Old Testament law
- Selective use of the New Testament
- Selection bias
- Confirmation bias