You've known him 6 months and now you know him even better. You know he chews tobacco. You know he hides things from you that you won't like. You know he'll disrespect you by doing something in your house he knows you don't approve of. I don't know much about the program but from what you post about what he said, you know he'll go against his program of recovery.
Dating is a fact finding mission and you just found out a whole bunch of them. That is a lot to digest.
You ask how to get past the feelings of betrayal and trust but I think that might be the wrong question. Maybe the question should be what kind of person do I want to date? Is he this person?
Those feelings are your internal warning system. I have vowed to never again ignore my gut feelings, or shush my inner voice. I spent years doing just that (and I have paid dearly for it) and I am trying very hard to be the person that honors that inner voice, and that makes decisions to protect it - because that voice is me.