In law school, I was in the Federalist Society. At that time the HLS chapter was in a phase of incredible growth (some of which was probably growth for growth's sake, in compensation for a preceding period of shrunken, fallow membership). On of the things stressed during this boom period was that the Fed Society was a "big tent": the members had a wide variety of political opinions, internal disagreement was frequent, etc. And to a certain extent this was true, although it didn't take long for me to be put off by some of the more common points of internal agreement, e.g. big-government conservatism with a generous helping of theocracy.*
The Fed Soc did put on a range of informative and interesting events, including many panel discussions reflecting the wide range of its members' positions. This was assisted by the refusal of many liberal faculty members to take part in Fed Soc panels; sometimes it's easier to invite a criminal-justice-skeptic libertarian to speak than to coax a left-wing professor thirty feet out of his office to defend a position he normally embraces. I assume they didn't want to validate the other panelists by participating in the discussion. Or something.
But the real problem with the Fed Soc is that even if the members go around telling themselves (and potential recruits) that it's ideologically diverse, nobody on the outside knows that---or buys it. So you get stuff like this, where a single line on a resume results in the hiring partner projecting heaven knows what onto a candidate. Might it be inconsistent, as one commenter noted, to hire someone at Legal Services who believes funding for Legal Services should be eliminated? Of course! However, it's not like joining a club in law school requires a blood oath to support everything that the organization supports, or what its prominent members support. (Maybe the applicant is a Ninth Amendment fan, or a gun rights maven, or pro-life---none of which are incompatible with the idea that poor people deserve legal representation or with BIGLAW litigation practice, and all of which are perfectly common reasons to be drawn to the Fed Soc.) Most people, though, don't think about that, or don't care. So whether the Fed Soc actually is a big tent is irrelevant; it's not perceived as one by outsiders, and so you can't count on that as a defense to any untrue suppositions people might make. You'll never get a chance to present that defense. The reviewers are just looking for a reason to toss your resume.
But what do I know, I'm just someone who quit disclosing** my Fed Soc membership*** after the first dozen times someone was flabbergasted to hear that I didn't support prayer in schools, sodomy laws, flat taxes, or hard time for drug users.
* By no means was this a universal position, but it was common enough to be troubling.
** This was not even the worst resume one-liner for me. The Harvard Law School Target Shooting Club was far more alienating. That got struck after EVERY single callback in NYC featured lengthy and fascinated/horrified discussion thereof. In the callbacks I got, that is.
*** Actually, I think my membership has lapsed.