Trying to keep this short, the main question is really in the title..
My sister and I have a conflict which began about eight months ago, and I am currently not talking to her. We're both in our 20's, financially independent and have our own apartments away from home.
I don't have a great relationship with my parents at the moment. On several occasions my parents have expressed support for her on this issue and ... not-support for me. (For what it's worth, I feel that most of the disapproval comes from incomplete information on their side and the fact that, unlike my sister, I no longer follow their religion - not because my choices are objectively wrong.)
Recently there was an attempt at a family get-together and both my sister and I cancelled (independently of each other, but at least on my end as a result of this conflict). When I told my mother she gave me a lecture. She's told me several times I need to talk to my sister and "figure it out". (I tried, it didn't end well, which is why I'm not talking to her now.)
As a kid, it seems reasonable to bring your parents in as mediators. "Mooom, she's being mean!" and then mom says who's right and makes you apologize and make up.
As an adult, I've avoided the subject with them. It seems gossipy at best. For instance I wouldn't involve a mutual friend, because I'm sure it would make them uncomfortable and it's not fair to throw them in the middle of it. So why would I do that to my parents! In contrast, from what my mother has told me, my sister confides in her and has talked to her about her side of this conflict.
So my question is what is a parent's role in sibling conflicts, when the siblings are independent adults? What's appropriate to talk to them about? How do I deal with my sibling telling them all about their side of it?