The responsiblities of all born again believers are the same, regardless of whether they are Jews or Gentiles. God has brought the two groups together to form 'one new man'--the body of Christ (Ephesians 2:14-16; 1 Corinthians 12:13).
Concerning the Sabbath, the Old Testament shadow has now been fulfilled in a New Testament reality. In Matthew 11:28 Jesus said, 'Come unto me and I will give you rest.' Today, Jesus Himself is the Sabbath. When we come to Him and live for Him, we are keeping the Sabbath. Believers are no longer required to set aside Friday evening through Saturday evening for the Lord; today every day is the Lord's day. The original Christians met together daily, not once a week (Acts 2:46).
For more on this subject, please read our article titled 'The Real Meaning of the Sabbath' found on the Traditions of Men shelf of the Apostolic Free Library.