Most evangelical Christians try very hard to follow the New Testament.
Firstly the New Testament is only part of the bible. Most of the book is dedicated to the Old Testament. So right out of the gate, "reading The Bible" includes a LOT of content you'd apparently prefer people NOT use when forming an opinion of Christianity. Is that right?
Secondly, evangelicals seem to be drawing an awful lot of their dogma from old testament teachings. The new testament says very little about gays for example, and most of the quotes evangelicals put forth are old testament.
Moreover, the 'big quotes' from the new testament are stuff like:
Matthew 5:43-44 Ye have heard that it hath been said, Thou shalt love thy neighbour, and hate thine enemy. But I say unto you, Love your enemies, bless them that curse you, do good to them that hate you, and pray for them which despitefully use you, and persecute you;
Matthew 7:12 Therefore all things whatsoever ye would that men should do to you, do ye even so to them: for this is the law and the prophets.
Matthew 22:37-40 Jesus said unto him, Thou shalt love the Lord thy God with all thy heart, and with all thy soul, and with all thy mind. This is the first and great commandment. And the second is like unto it, Thou shalt love thy neighbour as thyself. On these two commandments hang all the law and the prophets.
Its hard to reconcile that with pretty much everything people do today while claiming to be motivated by their "deeply held Christian faith", even today. From their views on homosexuality, gay marriage, illegal immigrants, torture, drone strikes, so called "stand your ground" laws and gun control in general, how they treat Muslim's, even Muslim American citizens, etc.