Non-academic activities do not count in any way towards graduate school applications unless they were successful or notable to a heroic degree. E.g. if you sold cupcakes as an undergraduate and made some money doing it -- or were popular at your church / club / frat's socials by doing it -- no one cares. If you sold your cupcake company for a million dollars, we'll care a bit: that's an exceptional level of competence and gumption, enough to reasonably expect that some of it will transfer over to whatever you put your mind to. Essentially, unless you're getting national media attention for your extracurricular activity, don't bother.
(Note: @jakebeal says "non-research-related". I think "non-academic" is more accurate: teaching / tutoring / TAing in your field is highly relevant. Being an active member in an economics club which, say, brings econ faculty to speak on campus is relevant, though not a game-changer. Also: please remember not to use "science" as a synecdoche for academia!)
Participation in "Greek organizations" is totally orthogonal -- I mean, has zero correlation; I MEAN: is completely irrelevant, either positively or negatively -- to graduate admissions. To be honest, I find the suggestion that it could be viewed negatively quite far-fetched: there is no "conflict of interest" here, any more than a Jewish or African-American or Republican student has a conflict of interest in their dealings with other Jewish or African-American or Republican students. An otherwise capable graduate student should be assumed to be capable of reasonable, professional behavior until evidence to the contrary comes up.
There is no reason to list this on any academic CV. As I said in a comment, the only real negative I see is that by putting something on a CV which is completely irrelevant, you show an ignorance of what academics think is important which makes you look less clueful about what graduate school is really about. It does so in such a mild way that I think almost any faculty member doing admissions would take it as a point of honor not to be influenced by this, but still: anyone who has read this question is now more clueful and knows to leave such things off an academic CV.
P.S.: Hold on:
I fear that that may also hurt my chances--either because the admission committee associates me with a rowdy chapter
So you think that the graduate faculty in the economics department will see your affiliation with, say, Alpha Omicron Pi and say "Well, some fraternities are fine, but not that one -- they're trouble!" Are you writing this question from the inside of an eighties movie? In the real world in 2016, the majority of faculty live far away from campus and have precisely zero dealings with Greek life including whatever incidents may occur on campus, and in many departments, at least a substantial minority of faculty were educated outside of the US and are thus completely unable to tell one Greek organization from another. As one data point: I live walking distance from campus and was educated in an American university with some amount of Greek life. Thus I happen to know that "AOPi" is a sorority rather than a fraternity. I would expect less than half of my colleagues to know that with any confidence. The local chapter of AoPi is two blocks from where I've lived for many years. What can I tell you about them as a group? Nothing. Don't care. Not my business.
