Both Marcion of Sinope and the Cathars discerned scriptures by examining the words of Jesus and Paul's epistles (the Cathars also used the larger canon that became the New Testament) and searched for apparent contradictions with the Old Testament, especially in terms of the nature of God. It appears that given the number of contradictions, and the fact that the Old Testament was seen as a unified work from one God, they came to the conclusion that the entire Old Testament was the creation of a Creator God that was different than the God that Jesus talked about.
In Marcion of Sinope's case, he also revised the Gospel of Luke to remove Old Testament links to Jesus to further support his view that Jesus was of a different God.
First off, it's worth noting that Marcion of Sinope, despite his heresies, is recognized as one of the first to propose a definitive list of New Testament scriptures. His original testamentum (Latin for "Testament") included ten of Paul's epistles and the Gospel of the Lord, which scholars recognize as the Gospel of Luke, but with edits Marcion made to remove references linking Jesus to the Old Testament God. For instance, he removed the chapters on the Nativity, likely due to the affirmations that Jesus fulfilled the Old Testament prophecies. Marcion also seems to have been the first to make a clear separation between the Jewish Scriptures and the Christian writings, asserting that they were separate entities and not a continuation.
Marcion created a commentary delineating the differences between the Old Testament and the New Testament along with commentary in a work titled Antithesis. That work has been lost to history, but scholar Daniel Mahar has created a rough reconstruction of it based on quotes from Marcion's critics (Mahar emphasizes several times that his version is loose and may not accurately reflect the actual contents of the original).
It appears that the general strategy Marcion used is to consider a New Testament passage, especially the words of Jesus, and find passages of the Old Testament that appear inconsistent with it. For instance, the New Testament passages:
God is light, and in Him is no darkness at all (1 John 1:5b) God is love (1 John 4:16); [Love] thinketh no evil (1 Corinthians 13:5d).
Contrasting with the Old Testament passages:
I form light, and create darkness: I make peace, and create evil: I the Lord Yahweh do all these things (Isaiah 45:7). Do they not err that devise evil? (Proverbs 14:22a)
(Note that not all Bible translations translate passages in this way. For instance, a number of translations of Isaiah 45:7 instead of "evil" have translations like "calamity", "woe", "disaster").
There were three major categories of contradictions that Marcion came to see between the Old Testament and New Testament:
- The Creator God and the Supreme God
- Of note, Marcion argues that creation is definitely the work of a God, and says that Jesus Christ revealed an "Old God", unknown to this creator God, who is more powerful, thus justifying why this Supreme God is apparently absent in the Old Testament.
- The Inconsistencies of the Creator God
- The Old Testament mentions God changing his mind (e.g. not destroying Ninevah after telling Jonah he would), and several passages could be interpreted as him having limited knowledge. In the Golden Calf incident, Marcion presents Moses as being better than the Old Testament God in convincing him not to have wrath on the people.
- The Two Christs
- The Old Testament prophecies suggested a more warlike Christ than what came. Thus the Creator God was promising one type of Christ while the Supreme God sent a different one in the form of Jesus.
- Note that in Marcion's Gospel of the Lord, he changed passages to remove the idea that the Old Testament prophets talked about him, or were otherwise in line with his teachings. For instance, Marcion changed Luke 24:25 "O foolish and hard of heart to believe in all that the prophets have spoken" was changed to "O foolish and hard of heart to believe in all that I have told you".
As far as I can tell, Marcion considered that, since the Creator God seemed to be present in so much of the Old Testament, he was present in all of it, especially given that the Jewish authorities asserted that the entirety of the Old Testament was about the Creator God.
Regarding the similar Catharism movement that came later, surviving works such as The Book of Two Principles indicated that they followed a similar hermeneutic of trying to find differences between the portrayal of God in the Old and New Testament and attributing them to two Gods, a good one of the spiritual realm and an evil one of the material realm, i.e. creation.