Here's what I think: You can develop passions when you realize that the problem you're onto is a meaningful one. I think when you truly believe that the solution you're trying to provide genuinely helps people, you grow a passion not for the specific domain your startup is working in, but rather for the idea of solving a big problem. Growing a deep interest in how a particular domain works is secondary and required in your pursuit to solve a problem.
I don't think anyone at Stripe has a genuine passion for the technicalities of online money transactions, but I do believe that they know they're addressing a huge pain-point that many, many people have been forced to deal with. They know their solution will be meaningful, and so they'll try to dig as deep as they can into that specific domain so that their product is better tailored for their given problem. I could be wrong. I think pg's recent essay on Schlep Blindness touches on this as well. If you develop a passion for solving problems, you might open your eyes to many, many more opportunities, versus if you directed your attention on finding that one domain that really sets your candle aflame.
But, I do struggle with that question on an almost daily basis. While what I stated should provide encouragement in that passions and deep interests can be developed, I can't say I'm not jealous of others I see who have seemed to genuinely take a liking to a specific subject, so much so that, startup or not, they'll chase their dream and be happy doing it.
Every moment we do not spend ourselves in a worthy cause is simply a moment not spent in a worthy clause. Each moment we are given, we get for free. It is up to us how we spend it. Throughout our lives, no matter how we spend it, we are given another in the very next instant.
Some startups weren't based on a specific idea. e.g. Woz and Jobs first had a go at blue boxes. HP and Sony began trying a few different products. The motivation was more like: to make something cool, make a business work. If you like, the "idea" had a wider scope than a specific product. I think it's fair to say they were passionate - as in crazy motivated - about that. e.g. Woz loved making cool electronic stuff; Jobs loved making a business out of that. It's not a specific idea; though I suppose you could say they were passionate about each specific idea in a general class.
I feel there are two parts to my own passion: (1) that there's an opportunity (problem, need, cool new idea) that would make a difference; and (2) that I could do it. That second one is very important. If I don't think it's within my reach, I won't feel excited. Maybe I'll even feel a little depressed and inadequate. That's why confidence (aka faith, hope, courage) is so important. pg noted a few times that not knowing how hard it is can be a blessing - that some very capable founders would have thought their achievement was beyond their ability if they knew the obstacles involved.
I think you can get better at predicting what you will and won't like over time. You learn what you do and don't like about different types of projects.
One obvious trick for startups it to solve a problem you have yourself that you truly and deeply want fixed.
When Zuck started Facebook he wasn't deeply passionate about "making the world a more open and connected place" neither was Larry Page about "organizing the world's information". Their passion grew into a grand vision out of a small kernel of interest. It's hard to predict in advance how big an idea can grow.