Question: "What does the Bible say about what foods we should eat (kosher)? Are there foods a Christian should avoid?"
Answer: Leviticus chapter 11 lists the dietary restrictions God gave to the nation of Israel. The dietary laws included prohibitions from eating pork, shellfish, most insects, and various other animals. The dietary rules were never intended to apply to anyone other than Israel. Jesus later declares all foods clean (Mark 7:19). God gave the apostle Peter a vision in which He declares concerning formerly unclean animals, “Do not call anything impure that God has made clean” (Acts 10:15). When Jesus died on the cross, He put an end to the Old Testament law (Romans 10:4; Galatians 3:24-26; Ephesians 2:15). This includes the laws regarding clean and unclean foods.
Romans 14:1-23 teaches us that not everyone is mature enough in their faith to accept the fact that all foods are clean. As a result, if you are with someone who would be offended by you eating “unclean” food – you should give up your right to do so as to not offend the other person. We have the right to eat whatever we want, but we do not have the right to offend other people, even if they are wrong. For the Christian in this age though, we have freedom to eat whatever we wish as long as it does not cause someone else to stumble.
The Bible is far more concerned with how much we eat than what we eat. Physical appetites are an analogy of our ability to control ourselves. If we are unable to control our eating habits we are probably also unable to control other habits such as those of the mind (lust, covetousness, unrighteous hatred/anger) and unable to keep our mouth from gossip or strife. We are not to let our appetites are control us rather than us controlling them. See Deuteronomy 21:20, Proverbs 23:2, 2 Peter 1:5-7, 2 Timothy 3:1-9, 2 Corinthians 10:5.