Strictly speaking, liberalism and conservatism are political ideologies (and they're often used very differently in different cultures - liberalism in its original sense is not a left-leaning ideology), and not religious categories.
The problem when mixing them with religion is that they often elevate one truth/good to the truth/good. For liberalism it is freedom, for conservatism is it to preserve the values of society, for progressivism it is progress, for socialism (in its various categories) it is social equality, etc.
Most religions, on the other hand, maintain that a balance of these are necessary for a good human life/society. They are all important. In my own religion, Catholicism, the Church should represent freedom, preserve what is good, help us progress towards a better state, and guide us towards greater social equality. As my professor in applied theology/religious practice said, "When the Church stops fighting for social justice and equality, the Church is just as dead as if She stopped believing in Christ or stopped celebrating the Sacraments".
For that reason, once political ideology is mixed with religion, people start seeing only one factor as being important. Hence you have religious conservatives holding their societal "values" (which are, to be honest, often despicable) as more important than fighting poverty. And religious liberals (in the American sense, which doesn't really correspond to neither "liberal" nor "socialist" in their original meanings - it's probably closer to what is traditionally called "social liberalism") who see fighting poverty, or personal freedom, as more important than preserving what is good in our society or was good in previous generations. From a Catholic perspective, this could be seen as "sectarian" - which comes from "sector", "part", meaning "only looking at a part, not the whole". It is the opposite of Catholicism, which could be translated as "of the whole" or "wholeness", among other things. In other words, there is no such thing as conservative or liberal Catholicism, since to elevate only one good over the others is inherently un-Catholic. At least according to the Church, these goods are equally important.
Personally, I am a social anarchist (probably more accurately an anarcho-communist, but that has little to do with communism in the sense most people think of it, so I stick with "social anarchism"), and a Catholic. But I am not a "social anarchist Catholic". While I think some changes/some goods are more urgently needed than others in our current society and political reality, I do not believe they are more important than the others in a philosophical or religious sense. While I believe my political beliefs come very close to the tenets of Catholic social teaching (obviously, Republicans would vehemently disagree), they may not fit as well with other teachings. But contrary to what theo-conservatives seem to think, no political system will ever be in full accord with Catholicism. It is simply impossible, at least in this world. And Catholicism isn't a monolithic entity - there are numerous theological traditions, all "orthodox" (as in, they're acceptable interpretations), and often they're in significant disagreement. And theologians even disagree over what's acceptable. Many would see my views on sexual morality (I'd be described as liberal since I see nothing whatsoever wrong with responsible sex between two consenting adult individuals of any gender, nor do I see anything wrong with gay couples getting children, etc) as "heterodox", while a surprising number of even "conservative" Catholics agree if no one's listening. It's impossible to create a "Catholic" political system when there's not even full agreement over what Catholicism is, other than the most central tenets. And even then, it would infringe on the rights of those who are not Catholic - and that would be contrary to Catholicism itself due to the supremacy of the conscience. That's the reason why few Catholic countries originally had "moral laws", while most Protestant countries did.
So to sum up, religion and political ideology are two different categories, and to mix them is not just dangerous, but contrary to (most) religion. For that reason, the notion of "liberal Christianity" or "conservative Christianity" is essentially oxymoronic; but sadly, people keep mixing political ideology and religion nonetheless.
