Historically feminism evolved out of Christianity, rooted in the basic concept of the equality of all people: "there is neither Jew nor Gentile, slave nor free, male nor female; for you are all one in Christ Jesus" (Gal 3:28). There are Biblical laws that seem odd to us now, but looking at the culture they were given to, they were incredibly progressive and set the stage for society to baby step to where it is today.
Christianity is compatible with feminism by definition. Feminism's definition is the advocacy of women's rights on the ground of the equality of the sexes. We have mostly achieved this as a society. Genesis 1:27 says "So God created mankind in his own image, in the image of God he created them; male and female he created them." This is saying men and women were created equal. Therefore, Christianity is compatible with feminism by its definition, not by how it is displayed in our society today.