The scriptures are clear with regard to clean and unclean meats, but does this verse actually say that meat and milk should not be eaten together? No, it does not. Then what does it say? It says that God's people should not seethe a kid in its mother's milk. "Seethe" is an old English word for "boil" or "stew."
Why would anyone ever consider cooking a young goat in its mother's milk? Why did God bring this to the Israelites' attention? Why would they even think of doing such a thing? Even if they did, what would be wrong with it?
According to various Bible commentaries, the pagans of that era and of that area had a fertility rite, which involved boiling a kid in its mother's milk and sprinkling the broth as a magic charm on their gardens and fields. They did this in the hope of increasing the yield of their crops. Here is what The Treasury of Scriptural Knowledge says about Exodus 23:19:
The true sense of this passage seems to be that assigned by Dr. Cudworth, from a MS. comment of a Karaïte Jew. "It was a custom with the ancient heathens, when they had gathered in all their fruits, to take a kid, and boil it in the dam's milk; and then in a magical way, to go about and sprinkle all their trees, and fields, and gardens, and orchards with it, thinking by these means, that they should make them fruitful, and bring forth more abundantly in the following year. Wherefore, God forbad his people, at the time of their in-gathering, to use any such superstitious or idolatrous rite.
God was warning His people against following this heathen custom. It actually had nothing to do with the dietary laws.
If we were so inclined, would it be permissible for us to boil a kid in its mother's milk? It is not likely that we would want to, but if we did, we would be "tempting" God (Deuteronomy 6:16; Malachi 3:15) and breaking one of His laws, one that is just as binding today as those regarding the holy days and tithing.
Finally, is it permissible to eat meat and milk products together? Yes, of course! In fact, God has always allowed it. Our Elder Brother—our example in righteousness—Jesus Christ, mixed the two in a meal prepared for Him by Abraham and Sarah, hundreds of years before Moses:
Then the LORD appeared to him by the terebinth trees of Mamre, as he was sitting in the tent door in the heat of the day. . . . So he took butter and milk and the calf which he had prepared, and set it before them; and he stood by them under the tree as they ate. (Genesis 18:1, 8)
Is it likely that Jesus Christ would have broken one of His own laws in the presence of His human servants?
Milk and Meat
Other Forerunner Commentary entries containing Exodus 23:19: