You can "leave behind", as in "I left that stuff behind me" (God, drugs/alcohol, bad friends) or.. I don't exactly know how to use this if you are trying to say what you are turning your back on, but you could definitely say it easier if you are just saying it about anything or if you are saying it about someone else. "He left all that stuff behind."
You can also say "Stopped believing in" something or "Stopped believing" someone who lies all the time, or you "gave up" something, but you can't really "give up" your friends, you can "give up on" your friends if they are into bad stuff and they won't change and you don't want to be a part of it... You can "give up on" God, or you can "give up" bad things like drugs/alcohol that you would "turn your back on."
I would like to give you more ways to say it about turning your back on people but I can't think of ways that don't have a meaning similar to "abandon" (To "turn your back on" someone means you could be abandoning them, if they need you, but if they are bad for you then you are doing something good.)