In my opinion, I think it's extremely selfish of (both) your parents to put their ideologies before their child's happiness. It seems they care more for how others see them then you both living your lives. Let's face it your parents aren't going to be there your whole life, whereas your partner probably will.
To me it's a no-brainer. As long as your sure this is someone you really want to be with.
That said though I do understand it can be difficult for some people, especially if you're still reliant on them which I know from experience is pretty common in Asian communities. I'd say wait until you both are in a position to become independent and then tell them to either deal with it or stop being a part of your lives. If they stop talking to you over this, they probably aren't worth keeping around anyway. I think they'll see sense however and realise something so trivial isn't worth loosing your child over.
I had an aunt in this position, although she was the hindu and her partner was muslim. When she told my mum, grandma and other aunt about how she wanted to marry him they were dead against it. She did it anyway. My mum boycotted the wedding. 12 years later they have 2 kids, my grandma visits them for 3 weeks every year and everyone is totally cool with it.
Good luck anyway.