This is great! Do you think if you were debt free you would feel differently? I know you've mentioned in other posts that you have a very large amount of student loan debt. That was my first hit, that it's too stressful for you to spend that kind of money on dates, since you have to pay off the student loans. I can understand that. Is she debt free?
I don't think you have to have all of the same interests and passions as a couple. If you enjoy eating meals together, spending time together, and have stimulating conversations, that's fantastic. You mentioned that you are physically attracted to each other, and have mutual respect. That's a big deal.
My ex used to LOVE to go out to eat. He would pay, and looked forward to going to a restaurant on the weekends. I made our meals at home. (I bought most of the groceries.) I realized that after working hard all week, he really LOVED driving to the mountains, going for a hike in nature, and sitting down to a meal in a restaurant. It was how he treated himself. My tendency was to want to save that money and cook something at home. I learned to go with it. (I love eating out, too...but I live on a budget.) It was really enjoyable.
It's hard for people to understand financial issues if they don't have debt. I'm debt free, but I remember the struggle I felt when I wasn't. Your girlfriend sounds like a great person. I hope you can work it out, if you are in love with her.