I need advice

You are putting your religious convictions as more important than your feelings for this girl, right from the start. So she had no chance! Be honest and tell her.

I was in a similar situation last year, and early this year. My ex is a Hindu and I'm a Christian. Although I don't give a shit about religion and I actually don't subscribe to anything religious, my family did not accept my ex. He has a Hindu name too... Vishal. And he is very religious. Some of my family members even cut me off too for choosing to be with him. In the end, I was hurt. I got cut off and Vishal couldn't deal with the stress so when I threatened to breakup with him because of everything that was going on, he took it seriously. Now, we don't speak and he has blocked me on everything. I'd say I dodged a bullet though. Tomorrow would be one month of no contact. :)

Well for starters you can stop wasting her time, since you know it’s never gonna last. Be honest with her and cut it off immediately. Dragging it out just because you like certain aspects of her character doesn’t mean it’ll ever change or be at the level you want it to be. Sit her down, or do whatever you’re comfortable with, just do it respectfully and cut off all formal contact afterwards.

You'll be doing her a favour by letting her go, based on the details you have provided here. The problem seems to be with you not knowing yourself and your values and you are just stringing her along.
Surely she deserves better.

First, you have to find yourself. Since you said you're religious, look deep within yourself. Then talk to her; if you can find peace with this relationship, let her stay. Otherwise, let her go.