Some important context before I start: I grew up in a very conservative place, the kind of town where everyone gets married at 18 or sometimes before, and many of the people I knew growing up now have 3 kids already. So when I was 14, I started dating "Jason". He was my neighbor and his parents were/are good friends with my parents. We talked about getting married and having a family, and everyone was sure we were going to (my parents, his parents, us, etc.).
But then when I was about 17, I came out as bi and kind of freaked out. I realized I wasn't ready to get married at 18 and wanted to explore dating women too. So, I broke up with Jason. He took it really hard, and started to spread some nasty rumors about me. His parents cut my whole family off after that, and my parents weren't exactly accepting of me either. So, as soon as I finished high school, I moved away, and my parents didn't talk to me for 6 months. Eventually they got in touch with me and we now have a kind of strained relationship, but it's really a work in progress.
During those terrible 6 months, I met my girlfriend "Nora". At first it was just a casual thing that neither of us were expecting to be long term since she's so much older than me, but it's sort of just happened that way. We get along really well and complement each other great. We never really fight and she takes really good care of me (she went through something kind of similar with her parents when she came out too). She's helped me get my life on track, and now I have a job and I'm going to school on the side.
In the last 6 months, I started staying over at her house a lot more (my apartment is tiny and she has a nice small house). Every now and then, my parents call me just to say hi, and I usually talk to them for 5 minutes. I used to not answer when I was at Nora's, but now that we hang out so much, I've started doing it a few times. But the other day, Nora got REALLY mad about it: she said she's seen how much pain I was in because of them and she can't stand the idea of me talking to them, especially around her.
I understand where she's coming from but they're my family and I want to try to repair. How do I get her to understand where I'm coming from and not freak out every time I talk to them?
TL;DR!
Family shunned me, met GF, started casual, now we spend a lot of time together, she can't understand me wanting to reconnect with my parents and gets mad at me about it