It is because of Messianic Judaism’s belief in Yeshua (Jesus). 
The “Messianic Judaism is Christianity” statement comes from Traditional Judaism, but you cannot blame them. This is understandable since the Crusades, the Inquisition, and the Holocaust were done in the name of "Jesus" and caused much suffering to the mainstream Jewish community.  

The Messianic Believer will follow the Sabbath, the Feasts, and the dietary instructions as written in the Torah. Christianity, typically, does not.