Turn, when inchoative, doesn't need into. The inchoative use is things like turn red or turn evil, meaning to develop a characteristic. This usually takes an adjective as object, but there are several uses where it takes a noun that describes a characteristic of a person, generally representing some sort of diametric change - moving from one thing to its opposite or complement. For example, a common metaphor for a criminal who has turned to working against crime would be:
He was a poacher turned gamekeeper.
A gamekeeper being one whose job it is, among other things, to stop poachers.
Turn traitor is one of these examples, appearing in Oxford as a set phrase. It is, however, the same structure as "turned gamekeeper" in the saying above. It means to develop the characteristics of "being a traitor".
Now, you can use to turn with an argument using into. A witch might turn someone into a toad, after all, or a good man turn into a monster (metaphorically, usually). However, in that case, you do need appropriate articles. Thus, if you want the turn into version, you want:
I believe you will never turn into a traitor.
That, however, suggests the person fundamentally changing, rather than simply betraying someone. They were not a traitor, and then they were, which might seem like the same meaning as turn traitor, but the nuance is definitely different. If someone turns X, it is a decision they have taken, a change in the course of their life perhaps, but if someone turns into X they have generally changed in some fundamental, deep way.