Question

The division of the law into Moral, Judicial, and Ceremonial requires the categorization of the Mosaic laws into at least one of these categories. I would be interested to know to which of the categories the dietary laws might belong.

Answer

A very helpful entrance into understanding the law of God is found in the Westminster Confession of Faith, Chapter 19. The whole chapter is worth reading (click here for the entire text of the WCF), but to get at your question, just one part will do:

Westminster Confession of Faith, Chapter 19.3:

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.

The dietary laws fall under the ceremonial law. They were designed to guide Israel to see that it was set apart, a holy people living for God and his glory, in a fallen world. While there were and are actual health benefits from some of the dietary restrictions, it was holiness which was the point because God was dwelling in the midst of his people. For instance, there were restrictions about eating creatures that feed on carrion. With some of those creatures, it could be physically unhealthy to eat them because of their diet, but the greater picture is that contact with the dead generally made a person defiled, that is, ceremonially unclean and thus unable to enter into God's presence. The reason for a sacrificial system is to allow us to come before our holy Creator leaving behind the defilement of sin.

Now that Jesus Christ has come, our entrance into the presence of God is not based on external things but on our coming to God through his appointed way (of which the ceremonial laws were pointers or signposts) which is through the blood of Christ (Heb. 9:8-14). It is impossible for the blood of bulls and goats to remove sin (Heb. 10:4) or keeping a kosher house to make us acceptable to God. This is why Christ himself declared all foods clean (Mark 7:19, Acts 10:9-16) and also why the apostle Paul warns against returning to dietary laws as a reversion to a shadow picturing Christ and a turning away from the real Christ (Col. 2:16-22).

Believers now have the best food, Jesus himself, who we see presented to us in the Lord's Supper. He is the ultimate 'diet', and, we might say, the only truly 'kosher' (that is, acceptable to God) meal.