It was never much of a problem for me.
I met my non-greek husband at the end of my junior year. I just dragged him along to all of my sorority's date parties and formals during senior year.
He was a little bothered by two things - rush and mixers. I just explained to him that I had to disappear, and that (in the case of mixers) no I wasn't going to hook up
I'm not sure that he understood, but he accepted it.