The Hebrew Roots movement (not to be confused with the Black Hebrew Israelites) teaches that the church has been corrupted by Greek and Roman influences, and we need to get back to our Hebrew beginnings. After all, Jesus and His disciples were Jews, so to be a good Christian, you must be a good Jew.
Hebrew Roots adherents, also known as Messianic Christians, believe Christ's death on the cross did not fulfill the Mosaic covenant, but renewed and expanded it. Therefore, you must keep the Sabbath on Saturday, celebrate Jewish feasts and festivals, and observe the dietary laws.
Boy, if there aren't scores of passages that directly respond to this!
Jesus declared all foods clean in Mark 7:19, and said it again to Peter in Acts 10:15. In Romans 14, Paul said not to be divided over opinions about days and food. And in Colossians 2:16 he warned about Judaizers who pass judgment over dietary laws and Jewish holy days. These were shadows of things to come which were fulfilled in Christ.
"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. For if your brother is grieved by what you eat, you are no longer walking in love. By what you eat, do not destroy the one for whom Christ died." Romans 14:14-15
"Therefore let no one pass judgment on you in questions of food and drink, or with regard to a festival or a new moon or a Sabbath. These are a shadow of the things to come, but the substance belongs to Christ." Colossians 2:16-17
If you point to such verses, or the whole books of Galatians and Hebrews, you'll likely be told the New Testament you read is corrupt. Hebrew Roots teachers reject historical definitions of biblical doctrines. Their answers are often long-winded, full of myth and speculation, and quarreling over words. They make non-essential issues essential, and teach righteousness by keeping the law.
Not all are that extreme, but there are still serious problems with telling people to keep the Old covenant as if it were a higher path. The Bible says the glory of the Mosaic covenant has come to an end, but the glory of Christ is forever. We're to be "ministers of a new covenant, not of the letter but of the Spirit. For the letter kills, but the Spirit gives life," when we understand the text.
For further study, read Romans 1-3, 2 Corinthians 4, and 1 Timothy 1 and 4:1-4.