You are confusing two different things.
Christianity is a religion. Jewish is an ethnic group.
A Jewish person can practice Christianity, or Buddhism, or be an atheist. Or they can practice Judaism. They still remain Jewish no matter which religion they practice.
A Christian is a person who practices Christianity as their belief system. A Christian (believer in Jesus), can be Black, White, Oriental, Native American, or they can be Jewish, Irish, Italian, Egyptian, Gypsy/Romani, etc etc etc.
I guess it depends on who you ask.
Practicing Jews do not accept the term Messianic Jew. One can not be a devout Christian and a devout Jew.
Judaism is a religion as is Christianity. They are opposing beliefs.
Jews were not thought of as a race before the Nazis and their genocidal predecessors. Making the term "Jewish" a race instead of a religion was a lie perpetrated by those who wanted to justify "genocide."