I had a partisan resume but certainly toned it down. I took off lesser affiliations (college clubs, law school clubs, general membership roles), downplayed internships, and dropped the names of people I didn't need to list. I also wound up getting a job with a firm that is of the exact opposite political leaning, and is well known for its bent.
I didn't say a partisan resume won't get you a job, but it's smarter to try to please the largest number of potential evaluators in a job process. It is wonderful that yours worked for you, but someone asked for advice. This is what I've heard from my career services office (I discussed my resume at length), what I heard directly from attorneys this summer, and what I've gleaned from other people's job search experience.
Fair enough on trying to give universal advice. I had successful interviews at well-known conservative firms, so, again, I think it just depends on how you spin it. However, if you hearken back to the OP's actual question, it is about whether or not she should take a 1L job that would reveal her political leanings, not about the degree to which she should purge her resume. My advice would be yes, she should, if it's a good job and will provide relevant legal experience. My career services office said the same, and that was my experience and the experience of many of my classmates. YMMV.
I think this is right on point.
Also, if you're seriously concerned about how your activities or past jobs may look to a particular employer, it may help to take a look at the kinds of pro bono work they've done. For instance, my firm has done some pretty major work for Planned Parenthood and on same sex marriage - I felt no need to sanitize my resume. I tend to agree with goalie on whether this is actually necessary at all, but for the risk-averse, this may be helpful.
If a firm has a seriously conservative reputation (or the only things you have on your resume are public interesty and you're interviewing with firms), talk with career services about how to frame things. After a couple of practice interviews I was able to talk about my progressive activist employment/extracurricular history in a way that highlighted skills and did some work to assuage concerns about how I'd fit in doing corporate law.