Why do Mormons eat pork when they believe in the Old Testament which forbids it?
The proscription against eating pork was part of the law of Moses, and it was in force for all the house of Israel until it was nullified by the Savior during his mortal sojourn. When He appeared to the Nephites on the American continent following his resurrection, He explained the fulfilling of the law of Moses as follows—
And now it came to pass that when Jesus had ended these sayings he cast his eyes round about on the multitude, and said unto them: Behold, ye have heard the things which I taught before I ascended to my Father; therefore, whoso remembereth these sayings of mine and doeth them, him will I raise up at the last day.
And it came to pass that when Jesus had said these words he perceived that there were some among them who marveled, and wondered what he would concerning the law of Moses; for they understood not the saying that old things had passed away, and that all things had become new.
And he said unto them: Marvel not that I said unto you that old things had passed away, and that all things had become new.
Behold, I say unto you that the law is fulfilled that was given unto Moses. Behold, I am he that gave the law, and I am he who covenanted with my people Israel; therefore, the law in me is fulfilled, for I have come to fulfil the law; therefore it hath an end.
Behold, I do not destroy the prophets, for as many as have not been fulfilled in me, verily I say unto you, shall all be fulfilled.
And because I said unto you that old things have passed away, I do not destroy that which hath been spoken concerning things which are to come.
For behold, the covenant which I have made with my people is not all fulfilled; but the law which was given unto Moses hath an end in me.
Behold, I am the law, and the light. Look unto me, and endure to the end, and ye shall live; for unto him that endureth to the end will I give eternal life (3 Ne 15:1-9).