First I must say that there are some people out there who do believe we should stick with the Mosaic Law and not consume "unclean" foods. A quick Google search will lead you to people with that point of view, and I respect them. If they feel God wants them to eat kosher then they should!
But for those like me, I will attempt to explain our reasons for not following the dietary rules given to Moses. I don't want anyone to assume it was just pure rebellion or a lackadaisical attitude on our parts.
1. I am not a Jew. Although it's true that we Christians tend to have a soft spot for the Ten Commandments and will often fight for its inclusion in our courthouse buildings when the ACLU tries to get rid of them, God actually gave the Law to Moses for the children of Israel.
For God's own reasons and not because of Abraham's, Isaac's, or Jacob's innate goodness, God chose this line to bring forth the Messiah, Jesus. God wanted His people to be set apart from the surrounding nations. The Israelites often failed miserably, worshiped idols, mistreated the poor, acted unjustly to other nations and broke the Law, but God sent prophets to warn them to turn back to Him. When they did, He restored them. When they refused, He punished them like any good parent would do.
Israel was to be different thus God gave them explicit rules to follow. The Law showed them how to live and also showed them they were not perfect enough to keep all the rules. It proved they needed a Savior, but that's a whole other topic. :)
From Exodus 19:
Then Moses went up to God, and the LORD called to him from the mountain and said, "This is what you are to say to the house of Jacob and what you are to tell the people of Israel: 4 'You yourselves have seen what I did to Egypt, and how I carried you on eagles' wings and brought you to myself. 5 Now if you obey me fully and keep my covenant, then out of all nations you will be my treasured possession. Although the whole earth is mine, 6 you will be for me a kingdom of priests and a holy nation.' These are the words you are to speak to the Israelites."
And Isaiah 49:
3 He said to me, "You are my servant,
Israel, in whom I will display my splendor."...
6 I will also make you a light for the Gentiles,
that you may bring my salvation to the ends of the earth."
2. Food doesn't make us 'unclean.' In Matthew 15 Jesus was asked why his disciples did not wash their hands before eating. After all this was breaking with tradition of the elders. Jesus replied,
11What goes into a man's mouth does not make him 'unclean,' but what comes out of his mouth, that is what makes him 'unclean.' "
17"Don't you see that whatever enters the mouth goes into the stomach and then out of the body? 18But the things that come out of the mouth come from the heart, and these make a man 'unclean.' 19For out of the heart come evil thoughts, murder, adultery, sexual immorality, theft, false testimony, slander. 20These are what make a man 'unclean'; but eating with unwashed hands does not make him 'unclean.' "
One might argue that Jesus was talking about unclean hands rather than food, however I believe the spirit of this teaching is that food and unwashed hands aren't what defile a person. Shrimp and bacon go in the mouth and out later as waste. The thoughts that come from within are what defile a person.
3. God purified all food. Peter was a good Jewish man. In fact when he received his vision, he was stunned and argued with God insisting there was nooooooo way he would ever eat something unclean!
9About noon the following day as they were on their journey and approaching the city, Peter went up on the roof to pray. 10He became hungry and wanted something to eat, and while the meal was being prepared, he fell into a trance. 11He saw heaven opened and something like a large sheet being let down to earth by its four corners. 12It contained all kinds of four-footed animals, as well as reptiles of the earth and birds of the air. 13Then a voice told him, "Get up, Peter. Kill and eat."
14"Surely not, Lord!" Peter replied. "I have never eaten anything impure or unclean."15The voice spoke to him a second time, "Do not call anything impure that God has made clean."
4. We are under a New Covenant. Many people believe Jesus fulfilled the Law perfectly and did away with our need for keeping it when he died and rose from the dead. He gave us the New Covenant so we are no longer bound by the Old Law in order to acquire salvation. The New Covenant is written upon our hearts and we have power to live this way through the indwelling Holy Spirit as we follow Jesus.
There are likely other reasons that people have, but these are the main ones for me. Another good passage to check out is Romans 14 which deals with people who argue over which days are special, which holidays to celebrate, which foods and drinks are acceptable. I love the freedom we have in Christ! Not that we are free to do evil, but we are free from the bondage of sin and enabled to do good through his wonderful power! How many of us can love our enemies by our own strength?