It takes time. A LOT of time. It’s a never-ending process, but it does get better.
What actually helped me the most was to question everything. I spent a lot of time in Al-Anon after I first left home (my mother is an alcoholic, too). In Al-Anon, I met people from every walk of life. Many of them were very kind-hearted but also very secular in their outlook. One of Al-Anon’s slogans is to “take what you like and leave the rest.” My sponsor, for example, didn’t believe in the Judeo-Christian idea of God, and, in fact, believed in a warm, loving, maternal, female god. (Not pagan, exactly–more a concept of a god than anything else.) Obviously, I disagreed with her on the theology aspect, but I examined my own beliefs in light of hers and readjusted mine where they no longer made sense.
For example, I thought of God as a kind of ancient boogeyman, lurking around the corner to jump on you when you did something wrong so that He could gleefully send you to Hell. Not true, of course, but when your parents are pretty much exactly like that, you get that idea about God. When she described her “god” to me, I liked some things about that “god” idea–someone who loved me very much and cared about me, someone who would protect me, someone who would sit with me when I was hurt–and asked myself why my God wasn’t like that. The answer, of course, was that He is like that; I was just conflating my experience with my parents as my understanding of God. As a result, I could see God as someone who loved me and cared for me unconditionally, and when the bad times came, as they inevitably did, I found it slightly easier to lean on Him.
Another thing that helped was talking about my experiences, especially to other people who also escaped. A lot of people who grew up in the sort of thinking that you described are, as another poster pointed out, very bitter about religion as a whole. What I needed to do was to talk to people who understood where I’d come from but who were still capable of seeing what little good there was in it. I don’t condemn all of Catholicism, for example, because my parents were very extreme examples of it: after all, I wouldn’t condemn any group for a few people in the group who didn’t follow its teachings well anyway, so why would I do so with religion?
I’ve mentioned before helping people who were in that movement to get out and start their own lives. That’s one of the most freeing and healing things for me. In any twelve-step program, the last part of it is to help other people find their way to healing and hope, and there’s a reason for that: it not only helps the person being helped, but it gives the helper hope, and we who come from abusive religious backgrounds but who want to continue drawing closer to God despite that really need hope.
On a practical note for discernment of sinfulness in an area, I have found two things to be helpful. For the more straightforward stuff (“Is birth control a sin?”) I use both research and logic to figure out the answer. So, for example, if I was asking if birth control is a sin (I use this topic just for an example), I’d read what the Church has to say about it (Humanae Vitae, etc) and then see if I had any rational arguments with it. If I do, I do more research or write out both sides to the argument. If I don’t, then I go with it.
For the less straightforward stuff (“Is this top too tight?” “Should I watch that movie?”) I have found it helpful to imagine what someone whose judgment I trust would say about the given subject. Probably sounds odd, but since in the family I grew up in a kiss onscreen between a married couple would be considered risqué, I know that my judgment about such things is off, so I try to model mine on someone who has a clearer picture of the whole thing.