Firstly; his behavior reflects badly on him, not on you. It's not your fault and people won't think it is (it took me a while for this to sink in too). Secondly; I can understand that your parents reaction is difficult. My mother started reading this book when she found out I was being abused. It helped her react to it all in a helpful way and made me feel less guilty about it all. Maybe you can show it to them? https://www.amazon.com/Helping-Her-Get-Free-Families/dp/1580051677
NTA.
Hey there, I saw your post on AITA. I am very sorry that you're going through this situation.
The issues between your BIL and you are 100% not your fault. Your sister is an abusive relationship. He is financially abusing her as far as your story conveys, and there's probably emotional abuse too. I went through a similar situation as a child where I had a useless, asshole stepdad that contributed nothing to the family that my mom kept trying to make work for years and years before the divorce.
Your situation as her sister is complicated. You see, the reason that BIL picks these fights with you is because he WANTS you gone... abusers isolate their victims from their support network so that it's easier to control them, especially if he senses that members of those network see them for what they are. The fact that you fight with him and call him out on his bullshit so much means he probably sees you as a threat to his relationship with your sister and wants you out of the picture. Of course, this doesn't mean that you have to babysit, you do have to put your own safety first after all.
I wanted to recommend a book designed for people just like you: It was originally called, "To Be An An Anchor In The Storm" by Susan Brewster. It is published today under the name, "Helping Her Get Free: A Guide for Families and Friends of Abused Women." It is an excellent book that can teach you what your sister is going through and how you can continue to support her while also protecting yourself.
https://smile.amazon.com/gp/product/1580051677/
I also encourage you to call a domestic violence hotline for advice about how to handle your sister. Talking to women in abusive relationships can be very frustrating because often they're deep in denial about how bad things really are because they're embarrassed to admit that they've "let themselves" get into a relationship like this and want to believe that they're strong enough to "fix" it on their own. As a result, they often lash out at and blame people who try to tell them the truth about how untenable their situation is. You will need support through this too, as I'm sorry to say that there will be no dealing with your sister in any way that doesn't involve a lot of sadness and frustration on your end.
I wish you luck. I am very sorry you're in this situation and I hope it all turns out for the best.
Also read this, BUT IMHO you need a stronger approach than what is advocated
http://www.amazon.com/Helping-Her-Get-Free-Families/dp/1580051677