Millennial women are favorable toward legal abortion, but less enthusiastic about the cause than their elders might expect.

A new Refinery 29-CBS News poll of women between 18 and 35 conducted in late July found less than a third, 28 percent, believe abortion should be legal in all cases. An additional 34 percent of women polled said it should be legal in most cases. Only 13 percent of millennial women believed abortion should be illegal in all cases. Another 25 percent said it should be illegal in most cases.

But while abortion is clearly the reigning top priority of the feminist movement, Refinery29 notes the poll found abortion "ranked surprisingly low on the list of priorities for all women." Surprising to media denizens, perhaps. "While 69% of women agreed Roe v. Wade should remain the law of the land, less than half (45% for millennials, and 44% for all age groups) said they were concerned about restrictions to abortion access," reported Refinery29 earlier this month.

Those ostensibly contrasting priorities could have something to do with the poll's revelation that 54 percent of millennial women do not consider themselves feminists. Forty-six percent do. The survey's margin of error among young women was 4.2 points, and 3 points among all age groups.

The feminist narrative is set largely by educated, urban women in the media and academia who tend to share monolithic opinions on abortion, which is in many ways shaped by their belief the cause is central to gender equality. The poll didn't ask women to rank the issues that matter most to them, but Gallup surveys this year have found about 1 percent of all people list abortion as the most important problem facing the country. Polls of the feminist community would probably come up with a much higher number.

A Morning Consult survey conducted this spring found only 4 percent of registered voters listed "women's issues" as a top policy issue overall. That might partially explain why it's difficult for a movement that excludes anyone who doesn't believe a war is being waged on women to connect with their target demographic.

[Also read: Millennial couples discuss money more than previous generations]

H/T Katie Yoder.