They have taken Jesus as Lord and claim to descend from the Jews in the
book of Acts. I have a friend who is into this up north and I am trying to
better understand this. They seem to thrive on the tenet that because NT
scripture points them back to the OT that they are to follow it (including
the law) with complete obedience.

Yes, I have studied out the issues extensively, both because I
have some very close friends who are converted Jews and because it is a
topic closely related to a book I am currently writing. You should be
aware that all the early disciples of Jesus were Messianic Jews.
Christianity’s first few years were entirely based in a Jewish context.
One can assume that until Jesus comes back, Jews will continue to come to
Christ.

The book of Acts and the book of Colossians will give you
useful and practical advice for relating to and understanding your Jewish
Christian friend. The early Jewish Christians did in fact continue to
practice much of their Jewish tradition–continuing to celebrate the
Jewish holidays, honoring the Sabbath and so forth. Colossians 2:16
teaches that we should not judge someone based on whether they observe a
particular Holy Day or a Sabbath or whether they do not. If your Jewish
friend chooses to observe the Sabbath or even some particular dietary law
as a matter of tradition of conscience, I would advise honoring that
practice and not judging that person in any way.

The problem which may arise is if your Jewish friend tells you
that you must also follow certain Old Testament laws in order to be a
really spiritual Christian. Here you will probably need to defend your
right to not be required to obey the Law of Moses for salvation. The
entire book of Galatians was written to address this problem, which was a
huge issue in the early church. Paul, in Galatians and Colossians roundly
condemns any attempts to force Jewish law on followers of Christ. If your
friend does this, you should do some careful study in Galatians and
Colossians with him or her.

Having said that, it may be a great idea for you to be open to
celebrating a Passover Seder or to learn some of the Jewish traditions
which are probably very valuable and important to your friend. Showing
that you are supportive and not judgmental will help your Jewish/Christian
friend understand where you are coming from. As Paul said, “To the Jews,
I became like a Jew to win the Jews.” (1 Cor 9:20). You would do well to
imitate the loving approach of Paul.

John Oakes