Jesus and the Apostles quoted from the OT hundreds of times in order to support what they were saying, so it doesn't work for someone to take the position that we should follow what they said but not what they considered to be an authoritative source. For example, Jesus quoted three times from Deuteronomy in order to defeat the temptations of Satan, which included saying that man shall not live by bread alone but by every word that comes from the moth of God, so he affirmed God as being being an authoritative source. In Deuteronomy 12:32, it is a sin to add to or subtract from the Law of Moses. In Deuteronomy 13, the way that God instructed to determine that someone is a false prophet who is not speaking for him is if they speak against obeying the Law of Moses, so there are not good grounds for interpreting Jesus or the Apostles as speaking against obeying what God spoke in Deuteronomy 14 in regard to refraining from eating unclean animals. If someone considers Jesus and the Apostles to be servants of God, then they should be opposed to interpreting them as speaking against obeying the Law of Moses, and if someone thinks that they should be interpreted as speaking against obeying the Law of Moses, then they should be opposed to considering them to be servants of God, but Deuteronomy 13 does not leave any room for anyone to consider them to be servant of God while also thinking that they should be interpreted as speaking against obeying the Law of Moses.DEUTORONOMY 14:6-8
6 And every beast that parteth the hoof, and cleaveth the cleft into two claws, and cheweth the cud among the beasts, that ye shall eat.
7 Nevertheless these ye shall not eat of them that chew the cud, or of them that divide the cloven hoof; as the camel, and the hare, and the coney: for they chew the cud, but divide not the hoof; therefore they are unclean unto you.
8 And the swine, because it divideth the hoof, yet cheweth not the cud, it is unclean unto you: ye shall not eat of their flesh, nor touch their dead carcase.
The Son is the radiance of God's glory and the exact likeness of His character traits (Hebrews 1:3), which he embodied through his works by setting a sinless example for us to follow of how to walk in obedience to the Law of Moses, so those who believe in the existence of the God who has the character traits that the Law of Moses was given in order to teach how to embody will express that belief through their works by following Christ's example of obedience to it.