I think it's safe to say that most Christians are far more shaped by feminist ideology than they realize.
The underlying assumption of the feminist movement is that men and women are not different in any meaningful way. As a result, society should treat men and women exactly the same. This is a manifestation of egalitarianism, which seeks to homogenize everyone and flatten out all of the diversity in God's creation. Thus, the feminist movement has always been in rebellion against God's word and God's design for masculinity and femininity. All the way back in 1848, the "Seneca Fall Declaration of Sentiments" denounced the way that churches barred women from holding offices such as pastor, elder, and deacon. The authors of that document (radical feminists Elizabeth Cady Stanton and Susan B. Anthony) specifically condemned church leaders for using the Bible to support their "chauvinistic" beliefs. From the beginning, the women's liberation movement was always about liberating women from the clear teaching of Scripture.
The sexual chaos we see all around us today is the bitter fruit that springs from the erroneous root of atheistic egalitarianism. If you say that women and men are completely interchangeable, then nobody should be surprised when the transgender movement gains tremendous popularity (see the book Irreversible Damage: The Transgender Craze Seducing Our Daughters). Transgenderism is the logical outworking of feminism. Nobody knows what a boy or girl is anymore, because the poison of the feminist agenda has been seeping into our churches and into our societal institutions for the past 175 years. Feminism has always been an attack on biblical femininity, but it's just now becoming so glaringly obvious that it can't be ignored. Transgendered men are now dominating all the fields in which the feminists fought for equality, but the feminists really have no argument as to why men shouldn't be allowed to do this. For example, women's athletics (esp. individual sports like cycling, swimming, weightlifting, and track and field) are being dominated by men. A man now holds the title for the highest earning woman in Jeopardy! history. Men are now appearing in the USA Today's "Women of the Year" list.
As we are currently witnessing, the "conservative" position called Complementarianism only pays lip service to the biblical view of men and women and is quickly collapsing (click here). This shows us that there is no alternative to God's Word that doesn't eventually descend into chaos, insanity, family disintegration, and societal death. The only way out of our mess is utter repentance and total submission to God's good design. For a basic overview, I highly recommend the books It's Good to Be a Man and The Fruit of Her Hands. If you want to understand the whole history and development of the feminist movement, I highly recommend the book Eve in Exile.