First, let me be clear; I am not implying that feminism must be accompanied by religious affiliation. However, I do feel that those who identify as Christians should not automatically reject feminist ideals simply because they don't perfectly align with traditional religious teachings. As a person of faith, I am aware of the contradictions between the Bible and modern-day activism, but adhering so strictly to theology can be dangerous. It is incredibly important to be open-minded and discerning, not only as a Christian but as an active member of society.
Most often when someone rejects feminism, it is based on the belief that the feminist movement has evolved into something excessive and radical. But at the very root of feminism is radicalism. In order to make the achievements they did (both socially and legislatively), early feminists had no choice but to be uncompromising and fanatical. That being said, I don't expect every feminist to adopt the same levels of extremism. I myself am a fairly passive feminist. What I do expect is for Christians not to dismiss the basic foundations of women's liberation or misconstrue its true goals.
A common misconception is that feminism no longer promotes equality of the sexes, but portrays men as the antagonists. Yet, feminists who shame men are no better than Christians who shame feminists. True feminists have a genuine respect for all sexes and sexualities.
Issues arise when feminists feel confined by the traditional roles Christianity has laid out for them. While most Christians acknowledge that expecting women to stay in the home and out of the workforce is an archaic way of thinking, some still believe that women should continue to 'submit' to their husbands. Though they may not mean 'submit' in the literal sense, Christian women are encouraged to make family their priority, if they so choose to have one. Certainly family should be a priority in anyone's life, but I find it unfair that men who also have families may prioritize work alongside them (in order to provide for them), while women continue to be stigmatized if they choose to do the same. Additionally, Christians view the man as the backbone of the household. Marriages and nuclear families outlined in the Bible continue to give men the upper-hand, even within the home. (These Christian households also exclude any other sort of non-traditional family (i.e. LGBTQ families), but that's an article for another time.) This is not to say women are not equally valued, but they are valued for different reasons, some of which don't always align with what some women envision for their futures.
The futures these women envision are not a rejection of Christianity. A woman who decides to join a profession and become the breadwinner, a woman who is naturally inclined to take the lead within the household rather than her husband, or a woman who simply decides to have no family at all, is not an offense to the church. Such simple (and extremely common) variations from the traditional path are a basic expression freedom- both as a woman and as a human being.
Plenty aspects of Christianity have phased out over time as humanity has acknowledged their inherent immorality (slavery, homosexuality, etc.) Feminism is no different. Women are finally beginning to make progress through feminism after being suppressed for so many years. It is imperative that we, as a people, remain aware of current social contexts and how religion should adapt to them. The core of Christianity will not change (nor should it), but its teachings should reflect the healthy advances society is making toward equality.