A minority of New Testament (NT) believers still adhere to the dietary laws of Leviticus 11 (e.g., Seventh-Day Adventists). Are they correct? Should we all be abstaining from pork, shellfish, and the other foods banned in Leviticus 11?

No. The NT clearly teaches that the distinction between clean and unclean meat is gone. Several passages teach this concept.

First is Acts 10:10-16 where Peter receives a vision from God:

And he became hungry and wanted something to eat, but while they were preparing it, he fell into a trance  and saw the heavens opened and something like a great sheet descending, being let down by its four corners upon the earth.  In it were all kinds of animals and reptiles and birds of the air.  And there came a voice to him: ‘Rise, Peter; kill and eat.’  But Peter said, ‘By no means, Lord; for I have never eaten anything that is common or unclean.’  And the voice came to him again a second time, ‘What God has made clean, do not call common.’  This happened three times, and the thing was taken up at once to heaven.

Second is Romans 14:14 where Paul states, “I know and am persuaded in the Lord Jesus that nothing is unclean in itself, but it is unclean for anyone who thinks it unclean.”

Third is 1 Timothy 4:1-5 where Paul writes,

Now the Spirit expressly says that in later times some will depart from the faith by devoting themselves to deceitful spirits and teachings of demons,  through the insincerity of liars whose consciences are seared,  who forbid marriage and require abstinence from foods that God created to be received with thanksgiving by those who believe and know the truth.  For everything created by God is good, and nothing is to be rejected if it is received with thanksgiving,  for it is made holy by the word of God and prayer.

Fourth, and most importantly, Jesus gives his views on clean and unclean foods in Mark 7:14-23:

And he called the people to him again and said to them, ‘Hear me, all of you, and understand:  There is nothing outside a person that by going into him can defile him, but the things that come out of a person are what defile him.’  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.)  And he said, ‘What comes out of a person is what defiles him.  For from within, out of the heart of man, come evil thoughts, sexual immorality, theft, murder, adultery,  coveting, wickedness, deceit, sensuality, envy, slander, pride, foolishness.  All these evil things come from within, and they defile a person.’

The bottom line is that Jesus and his apostles clearly proclaimed the dietary laws in Leviticus 11 to be null and void. Those laws were in force for national Israel, but upon the arrival of Jesus, they were abrogated for new covenant believers.