As other posts have indicated, "feminism" can denote many things.
Historically, in the US, there have been three waves of feminism thus far. First wave feminism involved the suffragettes fighting for women's right to vote. The vast majority of American Christians do not have issues with women voting. I don't know of any 21st century Christian groups that object to women voting. (There may be some highly conservative sects out there that would disapprove of it). However, at the time, it was *very* controversial. Women were told they had no need to vote because their husbands' or fathers' votes counted on their behalf. Another smaller part of first wave feminism involved opening some job markets for women. For example, teaching was advocated by some suffragettes as a noble profession for women. During the late 19th century, women (if they were single) were allowed to teach for half the pay that the male teachers received. (As an aside, this NEVER applied to poor women. Poor women have historically always worked outside of the home to help provide for their families--maiding, laundry, cooking, farming, factory work, etc.)
Which leads to second wave feminism. This happened in the 1960s and 70s in the US. During second wave feminism, women were fighting for greater opportunities in education and the workplace, equal pay, financial autonomy (the ability to have a credit card or a checking account without your husband on it), body autonomy (abortion rights, rights in sports, proper criminalization of sexual assault and harassment, etc.), political power (more women in office), etc. There was also the push for the ERA which would have made equality between the sexes in all areas a matter of the constitution. As you can see, this was a much more complex endeavor. While voting rights were clear-cut, there were several philosophical ideas in second wave feminism that required some cultural adaptation. At the time, there was a significant conservative religious pushback on many of these issues. Women like Phyllis Shlafly and Marabel Morgan asserted that women should not work outside of the home (although both of these women definitely had careers outside the home). As a result of second wave feminism, women can now: take on any occupation they chose, attend any higher-level educational institution they qualify for, have access to an abortion (more on this below), open a bank account, get credit cards, buy a house on their own, etc. The proliferation of women in formerly male-dominated fields--doctoring, lawyering, etc.--is a result of second wave feminism. Second wave feminism also led to greater awareness around issues of child care, divorce, domestic violence, sexual assault, pornography, etc.
Most 21st century Christians would be in agreement with much of second wave feminism. Only the most conservative of sects believe that women should not work outside the home, or that women should have limited education, or that women should allow their fathers/husbands to control all money/spending for them. Most American Christian women have benefitted from access to education, jobs, financial resources, etc., as a result of second wave feminism. Of course, the most contentious issue for Christians brought by second wave feminists is abortion. There's no need to explain here why many sects of Christianity object to abortion (nor do I want to get off-topic by doing so). Suffice it to say that this issue is so contentious that some Christians will not identify as feminist based on this issue alone.
The most current wave of feminism is referred to as third wave feminism. This is where most Christians (and people in general) find the greatest difficulties with feminism. Third wave feminism is more philosophical and diverse than previous waves. While some extreme views were mounted during second wave feminism (see Andrea Dworkin, for example), the extremes definitely get more press in third wave feminism. Many people characterize it as anti-male (and there are some elements of it that are this way). Third wave feminism has brought greater attention to sexual assault (the #metoo movement), domestic violence, body positivity, income inequality, etc. While many American Christians would agree with some of these ideas (most want justice for sexual assault and domestic violence victims, for example), there are nuances to many of these issues that some Christians object to. The variance and lack of focus for the movement as a whole causes some to feel that all feminists are anti-male, anti-family values, etc.
I hope this provides some useful information to you.