Christians are so stupid and hypocritical. How can they say they follow the Bible when they eat shellfish (Lev. 11:10), wear mixed fabric (Lev. 19:19), et cetera? They don't even know what that book says!
For example, this story about a man who tattoos a verse forbidding homosexuality on himself has been making the rounds recently. That the verse comes shortly before a prohibition against tattoos (Lev. 19:28) strikes non-Christians as the ultimate in idiotic hypocrisy.
To add to the confusion, would-be Christian apologists often provide defenses similar to this little nugget, left on that original post:
(As an aside, the tattoo situation seems incredibly hypocritical and unloving to me, too, albeit for different reasons — at the risk of falling victim to the same folly. But that's not the topic I want to address.)
Why do Christians "ignore" some parts of the law? Do the Old Testament laws have any bearing in our lives? Do we just pick and choose the things that seem easy, acceptable, or can we just ignore the whole lot?
Both responses given above are interesting, because they reveal a fundamental misunderstanding about the Law.
Chapter 19 of the Westminster Confession of Faith addresses this subject:
1. God gave to Adam a law, as a covenant of works, by which he bound him and all his posterity to personal, entire, exact, and perpetual obedience, promised life upon the fulfilling, and threatened death upon the breach of it, and endued him with power and ability to keep it.
2. This law, after his fall, continued to be a perfect rule of righteousness; and, as such, was delivered by God upon Mount Sinai, in ten commandments, and written in two tables: the first four commandments containing our duty towards God; and the other six, our duty to man.
3. Beside this law, commonly called moral, God was pleased to give to the people of Israel, as a church under age, ceremonial laws, containing several typical ordinances, partly of worship, prefiguring Christ, his graces, actions, sufferings, and benefits; and partly, holding forth divers instructions of moral duties. All which ceremonial laws are now abrogated, under the new testament.
4. To them also, as a body politic, he gave sundry judicial laws, which expired together with the State of that people; not obliging any other now, further than the general equity thereof may require.
5. The moral law doth forever bind all, as well justified persons as others, to the obedience thereof; and that, not only in regard of the matter contained in it, but also in respect of the authority of God the Creator, who gave it. Neither doth Christ, in the gospel, any way dissolve, but much strengthen this obligation.
Christ's death on the cross was the final sacrifice, so in Him the ceremonial laws that God established as part of temple worship have been fulfilled and abolished. Likewise, the judicial (civil) laws were given specifically for Israel as a political entity. So, as one Q&A puts it,
The civil laws of the Old Covenant (example: Lev. 25:29, "If a man sells a dwelling house in a walled city, he may redeem it within a year of its sale. For a full year he shall have the right of redemption.") are abolished and no longer binding on us, and the ceremonial laws (example: animal sacrifices and temple worship) are also no longer binding on the new covenant believer. But the one aspect that does carry over is the moral law (as summarized in the Ten Commandments), and we are bound to keep those.
This is an important distinction. We need no longer follow Kosher rules, wear only unblended fabric, or go outside the camp (except in the Hebrews 13 sense) because these rules have been fulfilled in Christ. But we're not similarly excused from following the 10 Commandments and the rest of the moral law.
Instead of looking for reasons to ignore the law, Christians will find it written on their hearts (Jeremiah 31:31-34). Not an iota of this law will pass away (Matt. 5:18). We're still called to keep in step with the Spirit (Gal. 5:16-25), and to speak and act as those being judged under the law of liberty (James 2:8-13). We have died to the law in order that we may bear fruit for God (Romans 7:1-6); God's grace was given us in order that we might do the good works he prepared for us (Eph. 2:8-10).
Update: Tim Keller just wrote similar things in Old Testament Law and The Charge of Inconsistency.