interviews

I doubt they ask that during the registration process and if they randomly do no sorority will find that out. One house is notorious for asking that question during rush because they care no one else does.

some houses will care a lot about what your family does/where you are from. That really just comes down to whether or not you can actually afford to be in a sorority. A lot of people think they can, join a house, and then drop because of dues. This happens ALL the time to EVERY house.
If you're from a place that's expensive to live like lake oswego (for example) they'll know you have money, which means you can afford the commitment of a house. If your parents make a lot of money, then the assumption is that your parents will help you pay for it.

I'm like you-- my parents don't have impressive jobs and I pay for everything on my own. Mine never even went to college. So I played up the fact that my parents always supported my brother and I going to college and taking advantage of that experience. I also mentioned that to afford college, I started working at a young age/continued to work in college. Things like that can help compensate for any concern that you can't afford being in a house. Show that you work hard, don't take things for granted, and are independent. I did that and a lot of great houses kept calling me back. Don't worry about it girl :)