"Modern Christianity," Klopsch wrote in an explanatory note in his red-letter Bible, "is striving zealously to draw nearer to the great Founder of the Faith. Setting aside mere human doctrines and theories regarding Him, it presses close to the Divine Presence, to gather from His own lips the definition of His mission to the world and His own revelation of the Father… The Red Letter Bible has been prepared and issued in the full conviction that it will meet the needs of the student, the worker, and the searchers after truth everywhere."
Some large-print Bibles omit red letters, however, because the visually-impaired have difficulty with it. Another difficulty with this is that the various red-letter Bibles do not agree 100% on which words should be attributed to Jesus and which should not. Notoriously some red letter editions have Acts 18:9,10 in black while others have it in red. This albeit that the first edition was entitled: "The New Testament… With All the Words Recorded Therein, as Having Been Spoken by Our Lord, Printed in Color". He tried unsuccessfully to copyright it in England as well as the USA.
In the first red-letter Bible, the words "universally accepted as the utterances of our Lord and Saviour" were printed in red. Old Testament passages that Jesus quoted or that were directly related to incidents to which he referred (with the relevant cross reference) were likewise printed in red. Old Testament verses containing prophetic references to Christ were identified with red stars. More recent editions have sometimes avoided the Old Testament because of the difficulties, should verses in the Song of Solomon be in red for instance? This is a problem of interpretation which can, ironically, undermine the proper Christ-centred interpretation of the Scriptures.
Klopsch meant it to emphasise the authority of the Scriptures: "The plan also possesses the advantage of showing how frequently and how extensively, on the Authority of Christ himself, the authenticity of the Old Testament is confirmed, thus greatly facilitating comparison and verification, and enabling the student to trace the connection between the Old and the New, link by link, passage by passage".
There is a difficulty, however, because it seems to elevate certain words above the rest. It seems to imply that they are more holy than what is printed in ordinary black ink. The whole of the Scriptures, especially in fact the Psalms, are the word of Christ. all scripture is given by inspiration of God, and is profitable... ." (2 Timothy 3:16)
The Jesus Seminar used a similar colored notation for their publication. They used historical criticism to come to a conclusion as to which statements in the Gospels were spoken by Jesus (notated in red), or inserted by later Biblical writers or editors (notated in black). This Higher Critical bible made use of the notion that we can differentiate the words of Christ and this way of printing the bible to undermine the authority and infallibility of Scripture.
The idea was to produce an edition of the gospels in which only the words that Jesus "really" said would be in red. On the basis of the voting of the committee the words were to be printed either red (Jesus said it) or black (Jesus didn't say it). Eventually, a four-color scheme was developed matched to the voting record.
Red: Jesus undoubtedly said this or something very like it.
Pink: Jesus probably said something like this.
Gray: Jesus did not say this, but the ideas contained in it are close to his own.
Black: Jesus did not say this; it represents the perspective or content of a later or different tradition.
They even brought in the apocryphal Gospel of Thomas and printed some of its sayings in red.
Now we also have the problem of liberal evangelicals calling themselves Red-Letter Christians. They do this in order to discount the normal evangelical politics that opposes abortion, homosexuality etc. They are left wing in their politics and liberal in their convictions. They are reinterpreting Scripture in a liberal way.
http://www.beliefnet.com/story/185/story_18562_2.html
Although well-meaning, this way of printing the Bible has created many problems and should be avoided. Thankfully the Trinitarian Bible Society have and continue to avoid it as a practice.