Is AUTHOR wrong in the post ? POST : My (21M) girlfriend's (21F) parents are both from Lebanon, and since she was young, have wanted her to marry a Muslim, Lebanese man. I'm very much not that - I'm white as snow and irreligious. She doesn't want to follow their wishes and was able to break off a marriage her parents tried to arrange for her in the past.  

Currently, she's making a half-hearted attempt to keep our relationship a secret from them. They know when we're out together and pretty much every time she says she's going to hang out with me, they ask her if we're dating, and she's been denying it, but they essentially know. I'm not 100% comfortable with this, but in my mind it's her decision how to deal with this, and because I don't know her parents or their culture I've just let her do her thing. I've told her that we may as well just come clean at this point, but I haven't pushed the issue.  
Of course, her parents aren't happy about this. They've yelled at her a few times over it and have generally expressed their displeasure. Thankfully they've never been violent. The worst that's happened is her dad tried to block her from leaving by standing in the door, but she just left through the back door.  
She says that she doesn't really care what her parents think or about her relationship with them, because as she has said, they try to control her and don't respect her. She's currently trying to move out but that may take a few months. Essentially, she's trying to avoid the drama of her openly dating a white guy until she moves out.  
Now, my parents know all about this, and my dad has essentially labeled me the asshole for causing conflict in her family. Basically, he's told me that, unless I expect to marry her, I should break it off, because family is everything. I have no idea if I'll marry her - we've been dating for a solid four months. In my mind, if I don't marry her and it's not me who causes conflict, it'd be her next boyfriend, unless he's a Lebanese Muslim. (A relevant detail is that I'm her first boyfriend since the guy they tried to get her to marry, who lived on a different continent for 90% of their engagement)  
So I guess my question is twofold - AITA for facilitating her not telling her parents we're dating, and AITA for dating her in the first place when, even if it were open, it would cause conflict with her parents?  
Tl;Dr I'm dating a girl whose parents are Lebanese. She's trying (kinda) to keep it a secret, but her parents basically know, and they are not happy. AITA for helping her keep it a secret, and AITA for dating her in the first place if it causes conflict?