From Catholic Answers “Quick Questions”:
**Q: Jehovah’s Witnesses told me that Jesus’ commands to eat his flesh and drink his blood in John 6 could not be literal because Jesus would be advocating something against God’s law by commanding us to eat blood (cf. Gen. 9:4, Acts 15:28-29). What can I say to this? **
A: You can say four things. First, any divine command that comes later modifies divine commands that came earlier. When Jesus declared all foods clean (Mark 7:19), his command superseded the earlier command that certain foods be regarded as unclean (Lev. 11:1-8). If Jesus today commands us to drink his blood, his command supersedes any prior command concerning drinking blood.
Second, the command against drinking blood, like all of the Old Testament dietary regulations, has passed away, for “These are only a shadow of what is to come, but the substance belongs to Christ. Therefore let no one pass judgment on you in questions of food and drink” (Col. 2:17, 16).
The mention of not eating blood in Acts 15:20, 29 was a pastoral provision suggested by James to keep Jews from being scandalized by the conduct of Gentile Christians. We know that these pastoral provisions were only temporary. One concerned abstaining from idol meat, yet later Paul says eating idol meat is okay so long as it doesn’t scandalize others (Rom. 14:1-14, 1 Cor. 8:1-13).
If it is objected that blood is not a food (though it is in some cultures), note that Jesus was asked (Mark 7:5) why his disciples ate with unwashed hands. He replied, “Don’t you see that nothing that enters a man from the outside can make him unclean? For it doesn’t go into his heart but into his stomach, and then out of his body” (7:18-19). In context this refers to a non-food substance (the dirt on one’s unwashed hands).
Third, the Old Testament is very specific about why one was not to eat blood: “The life of every creature is the blood of it; therefore I have said to the people of Israel, You shall not eat the blood of any creature, for the life of every creature is its blood” (Lev. 17:14, cf. Deut. 12:23). The Israelites could not eat animal blood because it contained the animal’s life, but there is one Person whose life you must have in you, “Christ who is your life” (Col. 3:4).
Finally, even if the Jehovah’s Witnesses were right that drinking blood were intrinsically evil instead of the subject of a temporary prohibition, they would still have problems with John 6 because, in their interpretation, Jesus would be commanding us to eat his flesh symbolically and to drink his blood symbolically. He would be commanding us to act out symbolically an intrinsically evil deed as part of a sacred worship service. But this leads us to a ludicrous conclusion, so it must be that drinking Christ’s blood is permissible (not to say desirable).