Sorority membership reflects the school’s make up and diversity. If the schools you are looking at are only 2-6% Asian, the sororities aren’t going to be more diverse than that. If you want more Asians, you need to look at schools in California or Texas or NYC, not in small rural areas.
I am in a sorority and both of my kids joined them too. One of my kids is also a Chinese adoptee but is 100% American (music, food, dress, friends), and she joined a chapter of my sorority. She was not the only Asian or the only adoptee in her chapter. There are only 3 sororities on her campus (only 27% of the students are women) and she received invitations to join all 3. IMO, race and looks had nothing to do with anyone receiving bids at that school.
If you look at the chapter photos from our chapters at MIT, RPI, Case Western, Yale, there are a lot of Asians because there are a lot of Asians at those schools. If you look at California chapters, you are going to see a lot of diversity but still a lot of blondes. If you look at Montana or Nebraska chapter photos, not a lot of diversity. If the school itself is diverse, the sororities are too. In the olden days when I was at school, there wasn’t a lot of racial diversity, but we really were a diverse group in religion, SES, and majors - we had a ton of engineers at a time when there weren’t a lot of women in engineering.
We lived in the south while my kids were in high school, and my Chinese daughter went to college in the south. It is different and there are still a lot of racial and religious issues, and people are excluded from clubs and activities. I felt we had to be aware of the issues but not changed because of them. We looked at one school and I just thought “no way” - too small, too rural, too ‘twin sweater set with pearls.’ There was a group of Chinese students on campus getting settled in over the summer to start classes in the fall, and I knew my daughter wouldn’t fit in with them either. They were Chinese and she was American.
My kids were raised in a world where Disney princesses included Jasmine and Mulan and Pocahontas. My kids never mention skin color when describing other humans but will say “the guy wearing the green shirt” or “the girl with the blond hair and glasses.” There are plenty of other kids in that generation who are the same, don’t see racial differences and look for similarities first when looking for friends at college. I was raised by Archie Bunker and have to struggle to not see race first, but they are a different generation.