"I have as much authority as the pope, only fewer people believe it."
- George Carlin
83% of Americans claim to be Christian. If you have a proposal you want supported, it is a great idea to tell people that what you're advocating is Christian. Given that 83% of Americans have not read the Bible, this gives you great liberty.
I don't mind the fact that the religious right have made up a new religion. People do that all the time - and inescapably so. Even if your intention is to conscientiously apply the words of the New Testament, you have to make judgments about what to take metaphorically and what to take literally. And of course conscientious Christians - like conscientious Jews and Muslims and Hindus and Buddhists - have to decide what to do in situations that Moses, Jesus, Mohammed, and Buddha could never have imagined (artificial insemination?), so creativity is inevitable. This is why we have over 40,000 religious denominations around the world.
I do mind that the religious right are Christians who essentially claim to understand Christianity better than Christ did. They are ignoring what he taught and making topics he ignored central to their religion. I think by that point you have an obligation to call yourself something other than Christian.
Jesus did not condemn homosexuality but he did condemn wealth. He did not condemn abortion but he did say that people will be judged by how they treated the least - and specifies that he's talking about the least as in people who are hungry, naked, and in prison, criminals and the destitute. Jesus made no mention of either abortion or homosexuality, leaving one to assume that it didn't really matter to him as much as turning the other cheek. Jesus did not ban alcohol. His first miracle was to make water into wine, and late at the wedding party after people had drunk quite a lot.
Paul seems to have condemned homosexuality (the verse cited is not really clear) and also condemned credit (this verse is really clear). Early in the 20th century, American clergy preached against consumer credit in the same way that they preached against homosexuality in the late 20th century.
So now people advocate a modern world with credit and standing armies and prison sentences for criminals instead of forgiveness and divorce and making alcohol illegal for people under 21 and the accumulation of wealth and all of that seems to me like progress. We ought to embrace that without pretending that it aligns with Christ's teaching, though. If you argue for such things, you can't just say, "It's Christian." You have to make your case (and by the way, there are pretty good cases for these.)
Meanwhile, if you want to claim that at the instant of conception that sperm and egg - human life that is not considered a human being - becomes a person, fine. Make your argument. But don't pretend that you are making it as a Christian, that something Christ said backs you on this point. Same with smaller government and the insistence that individuals not be supported by a welfare state. There are arguments for ignoring the poor but they stem from the teachings of people like Ayn Rand (who was an atheist) not Jesus. (There are religious arguments for not having a welfare state. As it turns out, the less financially secure people feel, the more likely they are to be religious. According to Jonathon Haidt, this is the primary reason that Americans are more religious than Europeans.)
I don't just have a problem with the religious right's insistence on bringing their religion into the public sphere. I have a problem with the fact that they've mis-labeled it as Christianity.