Not at all. While not all Christians would know to put it in such terms, there are two different types of "law" in Scripture: the Moral Law, which is absolute and unchanging; and other laws, the term for which I can never recall, which are given to specific peoples at specific times. The Moral Law is absolute and unchanging because it is tied to God's very nature, which is itself absolute and unchanging. A fairly good rule of thumb is that if it is directly related to one of the Ten Commandments, it's probably Moral Law. Other laws, such as the prohibition of eating certain foods or wearing certain fabrics, were given to the people of Israel at that specific time. It's hard to say for what reason God gave such laws—perhaps because certain animals were more likely to carry disease at the time, perhaps to set His chosen people apart from the surrounding pagan nations, perhaps for any number of other reasons—but the point is that such laws do not inherently reflect His nature. It was still sin for the Israelites to break such laws, not because it was immoral in and of itself, but because it meant disobeying the command of God. To break a Moral Law (to worship an idol, for instance) is immoral in and of itself.
In short, no, Christians (at least legitimate Christians) don't ignore parts of the Bible in favor of others. In fact, it's because we take Scripture as a whole that we see no need to follow the non-moral laws of the Old Testament.