Actually, in order to observe the Jewish dietary laws you would be required to "remove...words from the Bible" since the New Testament clearly deals with those laws. Remember that the dietary restrictions laid out in Leviticus centered around animals that were considered "clean" and those which were "unclean."
In Mark's Gospel account Jesus was speaking to the Religious Leaders about their requirements for ceremonial washing. They believed that if they didn't wash their hands in the prescribed way they would defile their food and thus become defiled. After recording that conversation Mark goes on to write:
And when he had entered the house and left the people, his disciples asked him about the parable. And he said to them, “Then are you also without understanding? Do you not see that whatever goes into a person from outside cannot defile him, since it enters not his heart but his stomach, and is expelled?” (Thus he declared all foods clean.) Mark 7:17-19 (ESV)
Obviously the point of our Lord's remarks was to say that true obedience results from a love of God from the heart— not the outward acts of keeping dietary laws. True holiness is internal. But just in case anyone might have missed the point, Mark went on to write: Thus he declared all foods clean.
Therefore, to go back and obligate people to the Levitical dietary laws you would have to remove these very words from the Bible.
Don't forget the story that's also recorded in Acts chapter 10 where Peter is specifically told to violate the Levitical dietary laws. God would never have done that unless those laws were no longer in force. (See Acts 10:9-15)
Finally we have the Apostle Paul's clear statement in his letter to the Romans where he declares: "...you are not under law but under grace." (Romans 6:14)
So it's impossible for the dietary laws to still be in force for believers since we are not under the Mosaic Law.