What does Susan Sarandon’s remark, “you can’t just vote your vagina” in distancing from Christine Quinn mean?

I’m often startled with, and at the same time enjoy finding unordinary expressions and quotes in Maureen Dowd’s column in New York Times. But I batted my eyes when I saw the actress, Susan Sarandon’s line, “You can’t just vote your vagina,” Dowd quoted in her August 20 NYT article under the title, “Bill’s turns at bat.”

http://www.nytimes.com/2013/08/21/opinion/dowd-bills-turn-at-bat.html?hp&_r=0

“Bill de Blasio, the 52-year-old public advocate has spent the last few days surrounded by the liberal glitterati of New York: Cynthia Nixon and her wife; “Boardwalk Empire” king Steve Buscemi; and ping-pong queen Susan Sarandon, who said she decided not to support Christine Quinn because “you can’t just vote your vagina.”

I’m confounded with the word; “vagina” being used in reference to vote and political decision and made by a female celebrity. What on the earth does it mean? Does it mean you can’t vote for someone simply because of the candidate being the same sex?

Are such rhetorical and public remarks as “you can’t just vote your vagina” accepted as a matter of course today?

During elections, it's hard to find an ideal candidate. For example, you might like someone's stance on tax reform, but shudder at their views on climate change. Put together a string of hot-button issues – in today's U.S. political climate, that would also include matters such as same-sex marriage, abortion rights, affirmative action, gun control, immigration reform, and legalized marijuana – and it can be hard (if not impossible) to find a candidate that you agree with on every issue. So, a voter must prioritize these issues, and determine which overriding factors will ultimately influence their vote.

Some "vote with their vagina" – that is, they belong to a voting bloc where, more than taxes, budgets cuts, and international affairs, what drives their vote is gender issues, which is often equated with reproductive rights. This means that proposed tighter restrictions on abortion would probably be the quickest way to lose this voter's support, although other gender issues, such as same-sex marriage or equal pay, are sometimes thrown into the mix.

For those who claim to vote this way, the language is deliberately shocking – it commands attention, in hopes to persuade politicians to (or dissuade politicians from) voting certain ways on certain issues, for fear of losing large-scale support.

I've noticed the phrase gaining traction in recent years; a search on Google yields over 600,000 results. (So, the answer to your bottom-line question is yes.) As one columnist wrote:

The choice is clear. We need to make this a single issue that we vote on. We cannot take our rights for granted or the war that was fought by our mothers, our grandmothers, and even our great grandmothers was fought in vain. We need to get out there and vote with our vaginas.

It seems understandable by the audience. I have never heard it. I expected a "with" but it is comparable to African American voting "black"

In her remarks, Sarandon, an outspoken liberal, flipped the script on vaginas at the voting booth. In 2012, it was conservatives who accused female Democrats of voting unthinkingly “with their lady parts.” It would be more accurate to say that liberal women were voting on behalf of their lady parts, which were are under not-insignificant threat, thanks to the GOP’s increasingly extreme views on reproductive rights

you can't just vote your vagina

means, as 'vagina' is by metonymy representative of femaleness, to vote because one is female and presumably a woman would be voting for a female candidate out of similar identity One could also presume that identity might lead one to vote for a male candidate but the context says otherwise.

So in context it says

you can't just vote for a woman because you are a woman, you need to look at what they stand for

Using gendered anatomical features is becoming more and more acceptable in public discourse.

To use 'with yu vagina' would make it too literal which is an awkward image.