In an nutshell and as was stated, a person born a Jew is a Jew for life and a person not born a Jew isn't a Jew until he goes through a formal conversion process. While one who adheres to certain tenets of Christianity is removed from the Jewish community (ie his "Jewish" status is compromised) he is still bound by Jewish law (assuming his adherence is a choice and not the result of an upbringing which deprived him of knowledge of his Jewish lineage).
As of (IIRC) the time of Paul who preached to the Gentiles, the notion of Christianity which might have initially been thought of as an offshoot or even sect of Judaism became one of a competing theology which replaced and rejected Judaism. Thus, historic Christians would not be considered Jews even if they chose to adopt some (most or all even) of Jewish beliefs. "Messianics" who want to have the title Jew are coopting the term and are not considered Jews unless they are so by birth.