Hillary Clinton grew up in a Methodist household, she taught Methodist Sunday school like her mother, is a member of a Senate prayer group, and regularly attends the Foundry United Methodist Church in Washington. Hillary Clinton can be placed in the moderate to liberal wing of American Christianity, but she appears to share a number of attitudes with more conservative American Christians. Clinton's liberalism is a relative matter: she's more liberal than many in America, and certainly more liberal than the Christian Right, but she has a long way to go to support truly progressive stances when it comes to religious debates.
The United Methodist Church is made up of both conservative and liberal congregations. The Foundry United Methodist Church in Washington which Hillary Clinton regularly attends describes itself as a "reconciling congregation." According to them, this means aside from not making any distinctions about race, ethnicity, or gender, they also invite "gay, lesbian, bisexual and transgender persons to share our faith, our community life and our ministries." The denomination as whole, however, regards homosexuality as "incompatible with Christian teaching" and opposes not only legalizing gay marriage, but even solemnizing same-sex civil unions.
Abortion is formally frowned upon by the United Methodist Church, but the denomination nevertheless opposes criminalizing abortion as a medical procedure. This makes it technically pro-choice rather than pro-life. America's temperance movement was once strongly supported by Methodist congregations and even today, the United Methodist Church formally affirms the importance of abstinence form alcohol in all forms — it's not even used during communion. The United Methodist Church takes a similarly strong stance against gambling in any form, including state lotteries.
For a while, the United Methodist Church was an important pillar of the Social Gospel Movement, a Christian social movement which sought to transform American politics and society along lines consistent with the Christian gospel. Hillary Clinton has stated that she believes it was an error for the Methodists to focus so much on social transformation because this took attention away from "questions of personal salvation and individual faith."
There is no evidence that Hillary Clinton's religiosity is superficial or an affectation; her behavior is consistent with her professed beliefs and she has explained more than once how important faith is for herself personally and her family. She has also said that prayer - trying to communicate with a god - is important in her life. The Christian Right, though, has tried to portray her as being just the opposite.
Radio show host Michael Savage, for example, has described her the most godless member of the Senate:
Then you have Hillary Clinton, the most Godless woman in the Senate, right out of the Marxist playbook, speaking at the National Hispanic Prayer Breakfast, so as all politicians, suddenly she becomes religious. And here she is opening up her speech to the Hispanics who actually believe in God...
Jerry Falwell once went further by declaring that she would energize the Republican "base" of conservative evangelicals even more than if Lucifer were running as the Democratic candidate for president. Demonizing Hillary Clinton transfers responsibility from the people who hate Hillary Clinton so much onto Hillary herself - if she's demonic, then people have no sane choice but to hate her. Furthermore, this ensures that there is no reason to hold back in attacks on her: you negotiate and compromise with political equals, not with demons.