Okay, first, let's get the Bible terminology straight. Hugo links here, which (except for some slight bashing of the UCC) gives some pretty neutral definitions of 'inerrant', 'infallible', 'literalist', and along the way, 'fundamentalist'. The difference between infallible and inerrant is a little too subtle for me at this point, but the idea seems to be that the Bible is absolutely correct on spiritual matters, 'revealing God, God's vision, God's purposes, and God's good news to us'. An inerrantist/infallibilist thinks that the Bible is the one and only spiritual handbook, though this does not mean it should not be read critically, as a complicated piece of literature. The contrast is with 'liberal' Christian denominations, like the UCC, who take the Bible to be at best a rough spiritual guide, divinely inspired but corrupted to an unknown extent by human interference.
Literalism takes inerrantism and infallibilism to an extreme: the Bible is right about everything, including all the bits that disagree with modern science and archaeology. So you can be an inerrantist/infallibilist without being a literalist, and still think the first two chapters of Genesis are to be read metaphorically, not literally, or disregard the misogyny and heterosexism of the Bible as irrelevant to its spiritual message. Fundamentalism is synonymous with literalism, where that has a conservative or even reactionary and theocratic interpretation. A fundamentalist Christian is politically conservative, reactionary, or theocratic, and cannot affirm evolution in good faith. Being evangelical means one has more 'flexibility', so an evangelical can be a creationist or believe in some kind of 'divinely-guided evolution', and be politically conservative (which is why a lot of fundamentalists are evangelicals, and vice versa) or politically liberal (which is why the terms are still distinct). From religioustolerance.org
In Christianity, the term fundamentalism is normally used to refer to the conservative part of evangelical Christianity, which is itself the most conservative wing of Protestant Christianity. Fundamentalist Christians typically believe that the Bible is inspired by God and is inerrant. They reject modern analysis of the Bible as a historical document written by authors who were attempting to promote their own evolving spiritual beliefs. Rather, they view the bible as the Word of God, internally consistent, and free of error.
Now, what is evangelism in itself? The term has ties to another name for the Gospels, the first four books of the New Testament, the account of the life and works of Christ. The word gospel means 'good news', and the bulk of these books is Christ's evangelizing: preaching and missionary work. Let's check religioustolerance.org's glossary of religious terms:
Evangelize: To gently explain ones beliefs to another in the hope that they might wish to adopt them. The word is sometimes used as a synonym for "Proselytize" -- to actively attempt to convert another person to your beliefs.
There's also this line in the definition of evangelicalism:
The name "evangelical" was originally used to refer to those faith groups which followed traditional Christian beliefs, in contrast with two other movements: philosophical rationalism and legalistic Christianity.
They also have a whole page of definitions. The three central components of all of these seem to be the following:
- Personalism -- This is a belief of intense personal faith and devotion to God, much like Kierkegaard's Knight of Faith, and in contrast to Kant's Enlightenment faith and Hegel's legalism.
- Activism -- As part of their devotion to God, the believer is compelled to share their faith with others, to literally evangelize.
- Biblicism -- The evangelical is an inerrantist/infallibilist about the Bible, whether this is in the narrow, literalist sense, or the broader sense discussed above.
So evangelicalism is entirely compatible with feminism, and liberal politics in general. Indeed, liberal evangelicals make the argument that Jesus talks a lot more about caring for the less fortunate than condemning homosexuality, and treated all of his followers, male and female, far more equally than sexist conservatives do.