Plenty of Messianic Jews go to services on Saturday if that's what you are talking about.
It is not REQUIRED for Gentiles to live according to the ceremonial aspects of the Mosaic Law, though.
These include days and dietary laws.
Other elements of the Mosaic Law are moral and nature, and a believer who is being conformed to the image of Jesus would not want to disobey those as they reflect the image of God.
But, believers are not Jews. Judaizers are those that claim this.
They claim that observing ceremonial elements like days and diet are required for the New Covenant believer. Some even go so far as to claim that you need to get your foreskin snipped to be acceptable to God.
Hogwash!
Those individuals are Judaizers and Paul anathematized them in Galatians.
If a Messianic Jew wants to continue observance of days and dietary elements of the Mosaic Covenant, without claiming others are required to observe them, this is fine, but those who claim all must observe them are Judaizers and fall under Paul's anathema.
Such individuals probably don't know Jesus, and thus don't know the Father. They don't believe in justification by faith alone, therefore they are accursed.
This is regardless of how religious they appear, with their external observances. Their heart has not been changed.