We HP and recruiting staff are very used to seeing people self identify on their resumes as gay, lesbian, member of certain minority groups, etc. No biggie in most big cities. In fact, we are told to increase diversity, so we are often looking for attorneys from diverse backgrounds. Our clients want diversity, many recruits want diversity, and we have to list our female/minority/gay/lesbian/transgender attorneys on various forms and surveys. So, self-disclosing may actually benefit you. And, if that is what you really want to do as a 1L, i.e. your dream 1L job, then go for it...but I caveat...
There will be some reviewers who will be biased. Of course, they are not supposed to be discriminating. If they turn you down because of your self-identifying, I would say you wouldn't want to work for that person or at that place anyway. The bigger issue -- and this applies not to alternative lifestyles but to any public interest gig -- is that the HP or other reviewer may wonder about your commitment and interest in working in BigLaw. We know most people do not make it to partnership, but we don't want someone who comes in ready to go. And, we wonder about whether someone who is so vested in certain issues could properly advocate/counsel clients who may have diverging interests. We don't like or agree with all our clients, but we have to represent them zealously within the confines of the law. Some years back, I interviewed a bright young woman from a top law school who had worked in many women-oriented organizations, women's advocacy, etc. She claimed she wanted to work in the employment practice of a law firm. I had my doubts about her ability/interest in representing employers (i.e., the clients) in defending them against the claims of say, a lady who alleged pregnancy discrimination. This candidate answered that she saw herself working on advising clients before any troubles, helping with employee handbooks and policies, etc. But I told her that kind of work was only a small part of what the employment lawyers did. Most of it was dog eat dog litigation. Someone alleges discrimination of some covered type. We defend them, usually digging up dirt on employee (e.g., falsified resume in first place, or sent email saying how much she enjoyed working with alleged nasty boss man). I ended up dinging the woman, not because of her work at a women's organization but because I did not see any even medium (not to mention long) term potential at the firm.
So, the long and short of it is that you will be outing yourself, but so be it. Just be aware that the public interest/private interest issue may arise. My advice would be to try to do some work at the organization that might translate in the private sector -- e.g., contract review, interviewing witnesses, drafting affidavits and declarations, research and drafting memoranda, etc. That way, when you write it up next summer on your resume, you will have substantive items to list and discuss that can go beyond the obvious public interest and that you can relate to your law firm interviewing.
I hope that helps. Please keep the good questions and comments coming. Oh, and do we have experienced attorneys out there as well as law students?