The specific set of laws that God has chosen to give teach us about the nature of who He is, for example, we can see that God is wise by seeing that He has given wise laws, we can see that God is holy by seeing that he has given holy laws, we can see that God is just by seeing that He has given just laws, and so forth. By doing what is wise, holy, just and so forth in obedience to God's laws we are testifying about the nature of who He is, and by doing that we are also expressing what we believe to be true about the nature of who He is, or in other words, we are believing in Him, hence God's command to be holy as He is holy. Likewise, by doing good works, we are testifying about God's goodness, which is why our good works bring glory to Him (Matthew 5:16), and testifying about God's goodness, we are also expressing the belief that God is good.
A different set of laws would corresponds to a different God with a different nature. For example, a God who commanded His people to commit adultery would have a different nature, set of character traits, or identity than that of the God of Israel. God's righteousness is eternal (Psalms 119:142), so any instructions that God has given for how to testify about His righteousness are eternal valid (Psalms 119:160), and the same is true for the other aspects of God's nature, including His holiness. It is contrary to the holiness of the God of Israel to eat unclean animals and if that were to ever change, then His holiness would not be eternal, and a God who does not command against eating unclean animals does not have the same eternal identity as the God of Israel. Someone who refuses to obey the God of Israel's instructions for how to be holy as He is holy lives in a way that testifies that the God that they follow is not holy.