I was in the same situation as you and your girlfriend when I rushed. We had a lot of long discussions about me actually rushing. He had a lot of the same concerns about it that you do. Ultimately, he said he trusted me and I should do whatever would make me happy. In the sorority that I chose, there was no hazing and definately no hazing having to do with guys. The only thing that he really had to adjust to were the mixers that we have every week (he is a jealous person to begin with). He finally realized that if I was going to meet another guy I would do it with or without the sorority and the mixers.
As for the time it takes to join a sorority, it does take a lot of time, especially the semester that you are rushing. This also bothered him a little bit, but it worked out. He ended up coming to visit me most of the time and if I had an activity for a little while on a weekend, he would either study or go visit some of his friends that went to my school.
Ultimately, the decision to rush or not to rush should be your girlfriend's. If you love, trust, and support each other as much as you say you do, then you should believe what she tells you about her sorority. Ask her questions about what she is doing with the sorority, but don't get jealous and give her the third degree about everything. Stay interested in her activites and support her...trust me, she'll appreciate it. Oh, also, make sure you have enough activites to fill your time so that you're not sitting around imagining all the things you think she could be doing that you wouldn't like. A lot of free time could make your imagination get the best of you.
To sum this up, I am now engaged to the guy I was dating when I rushed. He was my high school sweetheart and we have been together for 6 years now. We are getting married in September and I plan to have a few of my sorority sisters in my bridal party and invite even more. My only regret is that I didn't join my sorority sooner. So, this story has a happy ending.
I hope this has helpd you. Good luck and feel free to email me if you have any other questions and keep me updated.
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I am who I am.
Those who matter don't mind,
Those who mind don't matter.