I think the reality is whenever you have a majority versus a minority, it is natural for the minority to "band together". I am not talking just race, but religion, sexual preference, whatever. Because you are NOT in the majority, your rights are not always preservered. Therefore, as they say, strength in numbers.
I mean, it is natural for humans to divide themselves into groups. I went to a forum on the Black Diaspora in Latin America. One guy, who is Puerto Rican, is very white. When in the US, he identifies with other Puerto Ricans b/c they all share a similar heritage. When he goes home, he identifies with a smaller group, and not everyone. So, it's all relative.
And as to white people being accepted into non-white greeks, it happens. I myself am white and I am in an Asian Fraternity. I have a friend who is also white, and he is in Phi Beta Sigma, one of the Divine 9. It is not uncommon, and you are accepted. Once you join that organization, you are a brother or sister, respectively, and HOPEFULLY, that will transcend race, religion, etc.
I do know that Alpha Epsilon Pi has a National policy of only allowing Jewish people(correct me if I am wrong). However, certain chapters go against that policy(like Emory for example).
Frankly, people looked at me a bid when I first started hanging out with non white people, but you know what? Once the initial ice is broken and people see who you are, I personally have felt very little to almost none animosity.
Maybe it is because it is people of the majority showing interest in something that is NOT in the majority????
Ok, that's my opinion.