I guess every industry is different. While I may not always put SGRho on my resume, If I know the person I'm sending it to has a Greek affiliation, I'll put it on. If I don't put it on, there is always at least one activity on my resume that identifies me as a minority. I have found that this way I don't waste my time dealing with companies where this would be an issue. Also, sometimes self identifying can give you a leg up when a company is actively seeking to "diversify the workplace".
Bottom line, I suggest having several versions of your resume, so you can send the one most appropriate to your target audience.
That's just one poodle's opinion.