I've been dating a non-Greek for over a year now, and like your boyfriend, he is also very understanding about sorority life.
However, I don't think that the problem lies with dating a non-Greek. I think, from your post, the problem is simply managing time--and trying to juggle everything in your schedule. I think it's safe to say that many college students find themselves in that situation.
True, I've given up some things for other things, and I don't know if this'll work for anyone else except for me, but first and foremost I only take in what I can handle. You can't sacrifice loved ones, but I knew sorority life would be time consuming, so I became inactive in my other clubs and focused on school, the BF, sorority, and work. Social life is only allowed if there was time because really, it isn't that important to me. I take things as they come, and I don't worry too much about fitting everything in, because really--as long as I get my 7 hours of sleep, I know that I'll have good day.
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*I'm an Alpha Gam...Yes I am, Yes I am!*
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