I think the whole ”the old testament doesn't apply to me” line is basically a copout. If it's truly god's divine word, then you should follow the laws with the same vigor as any orthodox Jew. I'm familiar with all the debates surrounding the ”new covenant”, so we really don't have to lay out all the verses here, but I think we should be able to both agree that, this being a Bible discussion, there are just as many verses supporting the opposite view. Just look at the multiple new testament passages, particularly in Matthew, where Jesus himself specifically says that he hasn't come to supersede ”the Law”, meaning the Hebrew mosaic law. He goes out of his way to make this clear. Even later in Matthew when he makes the ”he who breaks the least of these commandments” statement, i'm paraphrasing but i'm sure you know the one. I get that mosaic law was written specifically for the Jews, but in a much larger sense, so was the entire Bible given the dynamics of the time period. The debate over whether or not there is a ”new covenant” goes back to the very beginning of christianity, and from what I understand it's attributed to Paul. His side of the argument obviously won out, allowing the religion an infinitely wider audience, but that doesn't make it the one right interpretation. Many Hebrew and Christian scholars and religious leaders at the time vehemently argued against it, and maintained that mosaic law still applied. Ultimately, if you reject mosaic law, then you might as well reject the entire old testament, and I doubt you do that (not assuming, just doubting).
To bring this back around to my original comparison of muslims and christians, it's worth pointing out that there's a similar debate within Islam as well. Not perfectly analogous, but enough so it makes my point. There are pays of the Quran which suggest that there are different shariah for different time periods (ie: old laws need not apply to modern times), while other verses assert the opposite, that the law is the law. Point being, muslims generally err on the side of safety and follow the old laws, while western Christians take the opposite route and err on the side of convenience, forcing the square peg into the round hole. It really doesn't matter which interpretation of either holy book is ”right”. What matters is that when given essentially the same choice as modern christians, muslims choose to follow the old laws because they actually fear their God. Because they actually believe he is real. If Christians had the same gut belief, they'd make the same choice.
This is my point. As a western Christian, you cherry-pick your contradictions to fit modern life. I'm not criticizing, I think it's great. Why? Because unlike you, I don't believe the civility of our society comes from Christian values. I think it comes from our secularism. I've read the Bible a few times, and I think I have a fairly good idea of what our society would look like if the 80% or so of Americans who call themselves Christian actually no-shit believed in their religion the way muslims believe in Islam. It doesn't look too fun.