It's an interesting argument that you're poised to set up: The dietary commands were intended to keep the Israelites and the nations from socially mixing, but now God does not want them separated, thus the dietary commands no longer have a function. I dispute that narrow of an understanding and the argumentative logic that follows it.
The purpose of the dietary restrictions doesn't appear to be to keep them from socially mixing. They appear to be about emulating God in His holiness -- to be holy as He is holy. Consider the following verses in sections dealing with dietary commands:
I am the Lord your God; consecrate yourselves and be holy, because I am holy. -- Lev. 11:44a (NIV)
I am the Lord, who brought you up out of Egypt to be your God; therefore be holy, because I am holy. -- Lev. 11:45 (NIV)
Even the verses you've shared, Lev. 20:25-26, say the same thing: We are to be holy because He is holy. Perhaps the emulation of God's holiness is related to the fact that unclean animals are not fit for sacrifice to God, so likewise they are not fit for human consumption. This idea becomes more pointed when you consider that unclean animals were unfit for the physical Temple where God's Spirit resided, and that our bodies are considered the Temple of the Spirit (1 Cor. 6:19).
But it's because of holiness, not specifically the dietary commands but dedication to the LORD in general, that the Israelites were set apart from the nations to be His. Earlier in the same chapter, the LORD says:
Consecrate yourselves and be holy, because I am the Lord your God. Keep my decrees and follow them. I am the Lord, who makes you holy. -- Lev. 20:7-8 (NIV)
So you see, that which made them holy (or in other words, set apart from the nations, since the Hebrew word for holy just means set apart [to the LORD]) is their dedication to the LORD and His ways -- to emulate the LORD; to be Holy as He is holy. And this set-apartness from the nations doesn't just come as a result of keeping the dietary commands, but essentially in following the LORD's voice in all of His ways. Lev. 20 includes lists of several other sins, including idolatry, paganism, and sexual immorality, by which avoiding they would be set apart from the nations as holy to the LORD.
There is a lot to read in the OT about holiness and set-apartness. And the NT writings continue the call to holiness: 2 Cor. 7:1, 1 Thes. 4:7, 2 Tim. 2:21, Heb. 12:14, 1 Peter 1:15-16, 1 Peter 2:9, et. al. There is also a lot to be said about the nation of Israelite purposed with being a light to the nations, through which the nations would be blessed, not a nation completely cloistered off from them. But maybe that's a discussion for another day...