Crappy,
The best teacher that I ever had was an Indian guy named Shashi. He was brilliant Phd from Princeton that ultimately chose to teach highschool math and physics for reasons that remain a mystery. Anyway, while he was my teacher he met the love of his life, the German teacher at the highschool. Like you he was extraordinarily nervous about introducing her to his very traditional family - she was white, divorced, etc. So they dated for a couple of years and decided to get married and he finally took her to meet his family. It went very, very badly. He chose to honor his family's wishes and immediately ended the relationship. I saw what it did to both of them for the next two years and it wasn't pretty. She eventually moved on, got married, had kids and is happy. I don't think he ever really recovered and last I saw him (some 5 years ago) he was still single and more of a recluse than he was before.
Bottom line, no one can really tell you what to do in your situation. My advice, follow your heart. Some of that is telling you to respect your parents wishes, some isn't. You need to figure out which part wins. My 2ยข, you're not going to spend the rest of your life living with your parents and you might just do that with Julie.