Do Messianic Jews believe that they should keep the Laws of Moses?
Yes and no. The Torah (or Law of Moses) is composed of the 613 Mitzvot, or Commandments, in the Tenach (Old Covenant or Testament) that God gave to Moses on Mount Sinai involving the festivals, the Ten Commandments, sacrifices, kashrut (kosher laws), etc. Generally speaking, Gentile Christianity today maintains that the Law is completely dead now that Yeshua has come and that we should have nothing to do with it.
But Yeshua tells us in Mathew 5:17-19
“Do not think that I have come to abolish the Laws or the Prophets: I have not come to abolish but to bring them to fulfillment. I tell you the truth, until heaven and earth disappear, not the smallest letter, not the least stoke of the pen, will by any means disappear from the Law until everything is accomplished. Anyone who breaks the least of these commandments and teaches others to do they same will be called least in the kingdom of heaven, but whoever practices and teaches these commands will be called great in the kingdom of heaven.”
We as Messianic Jews recognize that the Law was never made to get us into Heaven, but that it is a guide to follow to help us walk in the footsteps of Yeshua. The only way to be saved is through faith and grace of our Messiah.
Yeshua said “I am the way, and the truth and the life. No one comes to the Father except through me.” (John 14:6)
We must remember that all of the other Laws fall under the Ten Commandments and that they are now written on our hearts. (Jer. 31:31)