The Importance of Accepting and Obeying the Apostles' Teaching
Acts 2:42 - The first disciples "continued steadfastly in the apostles' doctrine." The teaching of the apostles was their standard of authority, because it was the word of God.
Luke 10:16 - If we accept the teaching of inspired prophets, we are listening to Jesus (because they taught His will). If we reject them, we reject Jesus and His Father, because Jesus and the Father guided them in what they taught. [This refers in context to the teaching of the 70, but the same would be true of the apostles' teaching.]
1 John 4:6 - Jesus called and sent the apostles to teach. They taught what God through the Holy Spirit guided them to teach. If we hear what they say, we are of God. Otherwise, we are not.
2 Corinthians 5:18-20 - Apostles and prophets were "ambassadors for Christ." They carried His message to the world instructing and urging men to be reconciled to God. As when a country sends an ambassador to another country, insulting an officially commissioned ambassador is insulting the one who sent him.
So the consequences that follow from accepting or rejecting the apostles' teaching are the same consequences as follow from accepting or rejecting Jesus' teaching, because they are the same teachings from the same source. Hence, we must respect the teachings of the apostles just as we do those of Jesus.
[2 Peter 3:2; James 2:10; Revelation 22:18,19; 2 Timothy 3:16,17]