I don't know of any part of the Bible where Jesus said it was ok to disregard the Old Testament dietary rules, so I would surmise that they were followed for a period after his death. When did that change happen though, and how?
I dealt a bit with this question in this post:
Simple version is that the Jewish dietary laws were part of the covenant between God and the Israelites. Christians are Gentiles and one does not have to become a Jew to become a Christian, and are outside of the Old Testament covenant, having their own covenant, the Crucifixion of Jesus.
Longer version is that the New Testament Book of Acts claims that James, Peter, and Paul agreed on this formulation in the Jerusalem Council:
Acts 15:23-29
"23 With them they sent the following letter:
The apostles and elders, your brothers,
To the Gentile believers in Antioch, Syria and Cilicia:
Greetings.
24 We have heard that some went out from us without our authorization and disturbed you, troubling your minds by what they said. 25 So we all agreed to choose some men and send them to you with our dear friends Barnabas and Paul— 26 men who have risked their lives for the name of our Lord Jesus Christ. 27 Therefore we are sending Judas and Silas to confirm by word of mouth what we are writing. 28 It seemed good to the Holy Spirit and to us not to burden you with anything beyond the following requirements: 29 You are to abstain from food sacrificed to idols, from blood, from the meat of strangled animals and from sexual immorality. You will do well to avoid these things.
Farewell."