Actually, it's not really shallow. Greeks are always doing things with other Greeks, so if you're dating a non-Greek it's a definite issue. Like dzsaidgirl said, lots of times non-Greeks don't understand that a mixer isn't about "hooking up" with members of the opposite sex. Since they can't attend themselves, they may feel jealous or insecure about what is going on at an event they aren't invited to.
I speak from experience: I dated a non-Greek guy for my last 2 years of college, and we got along perfectly until a social with a fraternity rolled around. Immediately, a fight began because my boyfriend didn't think that I should be going to an event with a bunch of guys. He just didn't understand that I was going to see my sisters and guy pals, and he didn't realize that as chapter president I was obligated to attend and represent my sorority.
My non-Greek guy also didn't understand why I spent so much time doing sorority events, and resented the time that I spent with my sisters. It didn't mean that he wasn't a terrific guy, he just didn't get the whole "Greek Life" deal.
I think it all depends on the individual. Some people can handle the fact that their significant others are Greek and will have Greek events to attend on a regular basis and some people can't handle it. The trick is to find someone who can!
I'm currently dating a non-Greek who is very supportive of my involvement in my sorority. Although I'm an alumna, I'm very active and do at least 1 activity a week with my sisters. During Rush, he rarely sees me because I'm an advisor to a collegiate DZ chapter! However, he handles everything very well.
For example, this summer, we had an alumni mixer with a Kappa Sig alumni group. I went, had a great time, and then had my boyfriend meet me after the event so that we could go out. It worked out perfectly.
When it comes down to it, I think that all relationships are based on trust. If your non-Greek boy/girl doesn't trust you to handle yourself well in a situation when he/she isn't around, then the relationship isn't a good one.