One could argue that evangelicals also "pick and choose their verses", not just the red-letter sayings of Jesus. In Acts, the post-resurrection Christians clearly have a "socialist" society, holding all things in common...so rigidly enforced by God that a couple who try to hold back some possessions meet the ultimate punishment. In Leviticus, the punishment for doing work on the Sabbath is as drastic as that for homosexual acts, yet I don't see them picketing state houses asking that we change the law so Wal-Mart is forced to close on Sundays. It's so much easier to use the Word to coerce other peoples' behavior, rather than to challenge our own.
BTW, putting the sayings of Jesus in red letters is based on scholarship that traces those sayings as being written down earlier than the Gospels, and therefore have a greater claim to absolute credibility. It is reasonable to discern a difference between the religion OF Jesus from the religion ABOUT Jesus.