Short answer:
No, you don't (ever) have to be a militant extremist like Putin.
Long(er) answer:
Just speaking from my own standpoint, I'd say support of equality, the empowerment of women, equal pay for equal work, more (and better) representation of women in the media, shattering the Glass Ceiling...I think it's safe to assume most (key word MOST) self-professed feminists will support most or all of those.
(I intentionally left out the abortion issue, as I've heard feminists sound off on both sides of the matter, and it often comes down to whether the person is a theist or atheist and, if a theist, when they believe life begins and so on, and that's really more in the court of atheism than feminism, though it's easy to see how the two do overlap here.)
I think there's a difference between what feminism was and what feminism is NOW--
Putin may hate to be styled as such, but I'd style him as being in line with an older, 1970s-era feminista guard, and that brand of more firebrand, often anti-establishment feminism is more and more being replaced rejected for a very, very important reason--
Women (finally!) ARE becoming part of the establishment, I mean, we have women in Congress, on the Supreme Court, female billionaires, and our Secretary of State is a female (until John Kerry takes over, anyway) and Hillary Clinton WAS the most serious female contender for the White House, and some think she might even try again in 2016 (though perhaps less so now.)
When you're disfranchised the way women were in the 1970s and before, it's easy to understand why a radical, wholesale anti-establishment course might be palatable, where every little thing is a big thing and a talking point and an opportunity for you to grow the movement through firebrand, hardcore, radicalized, attention-getting tactics.
That's no longer the case; that's no longer feminism, at least not as I agree with it and as my female friends agree with it...
They're all political, religious, and movement-oriented to different degrees, but I can't think of ANY of them that would agree with that sort of 1970s radicalism applied to this day and age, and I think most would agree with me equality, empowerment, and MORE women in the establishment is, loosely, what's needed more than destroying the establishment.
There's of course the idea of the Patriarchy, that we live in a male-dominated, male-centric, male-oriented world built on (Putin's about to get excited) the sort of ideological superstructure Marx talked about, and it's an ideological superstructure built around the ideas of men, by men, for men.
That concept is both true and untrue--again, it's somewhere in the middle now, in transition.
Do we live in a male-dominated society?
Oh, yes!
Are there no women in any considerable positions of power?
Oh, of course not! Australia's PM is a woman...England had Thatcher...Hillary...
Is the world (we'll keep to the West and leave the East/the Middle East alone) male-centric?
Yes, it still is?
Is it less so than what it was in 1970?
By a large margin!
Are things generally male-oriented?
It'd honestly depend on the thing/ideal/field you're talking about, some yes, some, not really.
Is the ideological superstructure of the West built around the ideas of men, by men, for men?
Yes and no...I mean, obviously, if you go back much further than, say, the 1830s at the earliest, you're going to have predominantly all-male authors, writers, etc., and while that's most of our ideological background, that also can't be undone...we can't know, as Virginia Woolf hypothesized, what a "Judith Shakespeare" might have written, and at the same time, we really can't get rid of Shakespeare...for that matter, as much as I don't believe it to be true and in many cases I find it immoral, we can't get rid of the Bible, either, not should we, that IS the West and IS part of the Western Tradition, and we should BUILD UPON and UPDATE that Tradition, not burn it all down or throw it all away...
On that note, then, take a look at the slew of great female authors SINCE the 1830s:
Austen came before then; not a huge fan, but she was undoubtedly talented and important...
To be fair, Charlotte Smith came before then as well, but didn't get attention until recently...
The Brontes, Emily, Anne, and Charlotte...
Emily Dickinson...
George Eliot, aka, Mary Ann Evans...
Virginia Woolf...
Edith Wharton, first woman to win a Pulitzer Prize...
Dorothy Parker...
Joyce Carol Oates...
Zora Neal Hurston...
Maya Angelou...
Angela Lansberry...
The 2011 Pulitzer Prize Winner was Jennifer Egan...
And let's not forget all the women with powerful positions in the film and magazine industries.
So the ideological superstructure IS still slanted towards men, no question, but also make no question in the fact that women have made considerable headway in the last 200 years, and that I don't think we really can say the ideological superstructure of the West is wholly a male one any more, it's not quite equal, but it's far more level and more diverse than it once was, and it's getting more friendly for feminists and minorities all the time.
There are A LOT of problems with the way women are depicted in TV and film--but not only has their been progress, but progress on top of progress.
Take a simple, easy-to-see example that everyone here should know...
The Original Star Trek. :)
Uhura was NOT the strongest female character in TOS at first , let's be honest...
It's a bit hard to do that while working the radio.
But she got better over time, and Nichelle Nichols actually kept playing the role because Martin Luther King, Jr. himself suggested she keep it up, citing her as a positive role model and the chance to create a better image of women and blacks on TV.
To that end, I think the character succeeded for her time.
And like the 2009 alternate universe movie or not...make no mistake:
Zoe Saldana's Uhura no longer is a passive person in the background wearing a short skirt and taking orders.
She was actively going around, doing things, berating Kirk and Spock...
She still had the short skirt, so that's not exactly progressive (to be fair, Chekov still had a silly over-the-top Russian accent, so some things are just part of the kitsch of the characters) but she was still far more active than 1960s Uhura ever was.
To continue on the pop culture kick, Hermione Granger is yet another intelligent, active female character we possibly wouldn't have gotten pre-1960s...and she's not just active, but saves the MEN, Harry and Ron, quite a few times in those movies and books...so that's a nice move away from the "damsel in distress" stereotype.
And so on.
So it's not yet totally a level playing field, but it IS getting better, there ARE positive depictions of women in the ideological superstructure that informs our cultural Western identity now and there ARE women in power, so the notion we should rail against the establishment seems ludicrous when, well, women are now, happily, PART OF IT FINALLY.
:)